Integrated Laplace and merged Merge remote-tracking branch 'gpy_real/devel' into merge_branch

Conflicts:
	GPy/core/gp.py
	GPy/likelihoods/__init__.py
	GPy/likelihoods/likelihood_functions.py
	GPy/likelihoods/link_functions.py

GPy/FAQ.txt

@@ -0,0 +1,8 @@
+Frequently Asked Questions
+--------------------------
+
+Unit tests are run through Travis-Ci. They can be run locally through entering the GPy route diretory and writing
+
+nosetests testing/
+
+Documentation is handled by Sphinx. To build the documentation:

GPy/coding_style_guide.txt

@@ -0,0 +1,10 @@
+In this text document we will describe coding conventions to be used in GPy to keep things consistent.
+
+All arrays containing data are two dimensional. The first dimension is the number of data, the second dimension is number of features. This keeps things consistent with the idea of a design matrix.
+
+Input matrices are either X or t, output matrices are Y.
+
+Input dimensionality is input_dim, output dimensionality is output_dim, number of data is num_data.
+
+Data sets are preprocessed in the datasets.py file. This file also records where the data set was obtained from in the dictionary stored in the file. Long term we should move this dictionary to sqlite or similar.
+

GPy/core/fitc.py

@@ -11,25 +11,27 @@ from sparse_gp import SparseGP
 
 class FITC(SparseGP):
     """
-    sparse FITC approximation
+
+    Sparse FITC approximation
 
     :param X: inputs
     :type X: np.ndarray (num_data x Q)
     :param likelihood: a likelihood instance, containing the observed data
     :type likelihood: GPy.likelihood.(Gaussian | EP)
-    :param kernel : the kernel (covariance function). See link kernels
+    :param kernel: the kernel (covariance function). See link kernels
     :type kernel: a GPy.kern.kern instance
     :param Z: inducing inputs (optional, see note)
     :type Z: np.ndarray (M x Q) | None
-    :param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
+    :param normalize_(X|Y): whether to normalize the data before computing (predictions will be in original scales)
     :type normalize_(X|Y): bool
+
     """
 
     def __init__(self, X, likelihood, kernel, Z, normalize_X=False):
         SparseGP.__init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False)
         assert self.output_dim == 1, "FITC model is not defined for handling multiple outputs"
 
-    def update_likelihood_approximation(self):
+    def update_likelihood_approximation(self, **kwargs):
         """
         Approximates a non-Gaussian likelihood using Expectation Propagation
 
@@ -37,7 +39,7 @@ class FITC(SparseGP):
         this function does nothing
         """
         self.likelihood.restart()
-        self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
+        self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0, **kwargs)
         self._set_params(self._get_params())
 
     def _compute_kernel_matrices(self):
@@ -120,7 +122,7 @@ class FITC(SparseGP):
             _dKmm = .5*(V_n**2 + alpha_n + gamma_n**2 - 2.*gamma_k) * K_pp_K #Diag_dD_dKmm
             self._dpsi1_dtheta += self.kern.dK_dtheta(_dpsi1,self.X[i:i+1,:],self.Z)
             self._dKmm_dtheta += self.kern.dK_dtheta(_dKmm,self.Z)
-            self._dKmm_dX += 2.*self.kern.dK_dX(_dKmm ,self.Z)
+            self._dKmm_dX += self.kern.dK_dX(_dKmm ,self.Z)
             self._dpsi1_dX += self.kern.dK_dX(_dpsi1.T,self.Z,self.X[i:i+1,:])
 
         # the partial derivative vector for the likelihood
@@ -140,7 +142,6 @@ class FITC(SparseGP):
 
             dA_dnoise = 0.5 * self.input_dim * (dbstar_dnoise/self.beta_star).sum() - 0.5 * self.input_dim * np.sum(self.likelihood.Y**2 * dbstar_dnoise)
             dC_dnoise = -0.5 * np.sum(mdot(self.LBi.T,self.LBi,Lmi_psi1) *  Lmi_psi1 * dbstar_dnoise.T)
-            dC_dnoise = -0.5 * np.sum(mdot(self.LBi.T,self.LBi,Lmi_psi1) *  Lmi_psi1 * dbstar_dnoise.T)
 
             dD_dnoise_1 =  mdot(self.V_star*LBiLmipsi1.T,LBiLmipsi1*dbstar_dnoise.T*self.likelihood.Y.T)
             alpha = mdot(LBiLmipsi1,self.V_star)
@@ -174,7 +175,7 @@ class FITC(SparseGP):
 
     def dL_dZ(self):
         dL_dZ = self.kern.dK_dX(self._dL_dpsi1.T,self.Z,self.X)
-        dL_dZ += 2. * self.kern.dK_dX(self._dL_dKmm,X=self.Z)
+        dL_dZ += self.kern.dK_dX(self._dL_dKmm,X=self.Z)
         dL_dZ += self._dpsi1_dX
         dL_dZ += self._dKmm_dX
         return dL_dZ

GPy/core/gp.py

@@ -15,20 +15,17 @@ class GP(GPBase):
 
     :param X: input observations
     :param kernel: a GPy kernel, defaults to rbf+white
-    :parm likelihood: a GPy likelihood
+    :param likelihood: a GPy likelihood
     :param normalize_X:  whether to normalize the input data before computing (predictions will be in original scales)
     :type normalize_X: False|True
     :rtype: model object
-    :param epsilon_ep: convergence criterion for the Expectation Propagation algorithm, defaults to 0.1
-    :param powerep: power-EP parameters [$\eta$,$\delta$], defaults to [1.,1.]
-    :type powerep: list
 
     .. Note:: Multiple independent outputs are allowed using columns of Y
 
     """
     def __init__(self, X, likelihood, kernel, normalize_X=False):
         GPBase.__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
-        self._set_params(self._get_params())
+        self.update_likelihood_approximation()
 
     def getstate(self):
         return GPBase.getstate(self)
@@ -38,15 +35,19 @@ class GP(GPBase):
         self._set_params(self._get_params())
 
     def _set_params(self, p):
-        self.kern._set_params_transformed(p[:self.kern.num_params_transformed()])
+        new_kern_params = p[:self.kern.num_params_transformed()]
-        self.likelihood._set_params(p[self.kern.num_params_transformed():])
+        new_likelihood_params = p[self.kern.num_params_transformed():]
+        old_likelihood_params = self.likelihood._get_params()
 
-        #TODO: Need to get rid of this check and think of a nicer OO way
+        self.kern._set_params_transformed(new_kern_params)
-        if isinstance(self.likelihood, Laplace):
+        self.likelihood._set_params_transformed(new_likelihood_params)
-            self.likelihood.fit_full(self.kern.K(self.X))
-            self.likelihood._set_params(self.likelihood._get_params())
 
         self.K = self.kern.K(self.X)
+
+        #Re fit likelihood approximation (if it is an approx), as parameters have changed
+        if isinstance(self.likelihood, Laplace):
+            self.likelihood.fit_full(self.K)
+
         self.K += self.likelihood.covariance_matrix
 
         self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K)
@@ -63,6 +64,10 @@ class GP(GPBase):
             tmp, _ = dpotrs(self.L, np.asfortranarray(tmp.T), lower=1)
             self.dL_dK = 0.5 * (tmp - self.output_dim * self.Ki)
 
+        #Adding dZ_dK (0 for a non-approximate likelihood, compensates for
+        #additional gradients of K when log-likelihood has non-zero Z term)
+        self.dL_dK += self.likelihood.dZ_dK
+
     def _get_params(self):
         return np.hstack((self.kern._get_params_transformed(), self.likelihood._get_params()))
 
@@ -70,7 +75,7 @@ class GP(GPBase):
     def _get_param_names(self):
         return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
 
-    def update_likelihood_approximation(self):
+    def update_likelihood_approximation(self, **kwargs):
         """
         Approximates a non-gaussian likelihood using Expectation Propagation
 
@@ -78,7 +83,7 @@ class GP(GPBase):
         this function does nothing
         """
         self.likelihood.restart()
-        self.likelihood.fit_full(self.kern.K(self.X))
+        self.likelihood.fit_full(self.kern.K(self.X), **kwargs)
         self._set_params(self._get_params()) # update the GP
 
     def _model_fit_term(self):
@@ -103,25 +108,13 @@ class GP(GPBase):
         return (-0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) -
             0.5 * self.output_dim * self.K_logdet + self._model_fit_term() + self.likelihood.Z)
 
-
     def _log_likelihood_gradients(self):
         """
         The gradient of all parameters.
 
         Note, we use the chain rule: dL_dtheta = dL_dK * d_K_dtheta
         """
-        dL_dthetaK = self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X)
+        return np.hstack((self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X), self.likelihood._gradients(partial=np.diag(self.dL_dK))))
-        #Think of OO way of doing this also
-        if isinstance(self.likelihood, Laplace):
-            #self.likelihood.fit_full(self.kern.K(self.X))
-            #self.likelihood._set_params(self.likelihood._get_params())
-            dK_dthetaK = self.kern.dK_dtheta
-            dL_dthetaK = self.likelihood._Kgradients(dK_dthetaK, self.X.copy())
-            dL_dthetaL = self.likelihood._gradients(partial=np.diag(self.dL_dK))
-        else:
-            dL_dthetaL = self.likelihood._gradients(partial=np.diag(self.dL_dK))
-
-        return np.hstack((dL_dthetaK, dL_dthetaL))
 
     def _raw_predict(self, _Xnew, which_parts='all', full_cov=False, stop=False):
         """
@@ -146,17 +139,16 @@ class GP(GPBase):
     def predict(self, Xnew, which_parts='all', full_cov=False, likelihood_args=dict()):
         """
         Predict the function(s) at the new point(s) Xnew.
-        Arguments
+
-        ---------
         :param Xnew: The points at which to make a prediction
         :type Xnew: np.ndarray, Nnew x self.input_dim
         :param which_parts:  specifies which outputs kernel(s) to use in prediction
         :type which_parts: ('all', list of bools)
-        :param full_cov: whether to return the folll covariance matrix, or just the diagonal
+        :param full_cov: whether to return the full covariance matrix, or just the diagonal
         :type full_cov: bool
-        :rtype: posterior mean,  a Numpy array, Nnew x self.input_dim
+        :returns: mean: posterior mean,  a Numpy array, Nnew x self.input_dim
-        :rtype: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
+        :returns: var: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
-        :rtype: lower and upper boundaries of the 95% confidence intervals, Numpy arrays,  Nnew x self.input_dim
+        :returns: lower and upper boundaries of the 95% confidence intervals, Numpy arrays,  Nnew x self.input_dim
 
 
            If full_cov and self.input_dim > 1, the return shape of var is Nnew x Nnew x self.input_dim. If self.input_dim == 1, the return shape is Nnew x Nnew.
@@ -169,5 +161,69 @@ class GP(GPBase):
 
         # now push through likelihood
         mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov, **likelihood_args)
-
         return mean, var, _025pm, _975pm
+
+    def predict_single_output(self, Xnew, output=0, which_parts='all', full_cov=False):
+        """
+        For a specific output, predict the function at the new point(s) Xnew.
+
+        :param Xnew: The points at which to make a prediction
+        :type Xnew: np.ndarray, Nnew x self.input_dim
+        :param output: output to predict
+        :type output: integer in {0,..., num_outputs-1}
+        :param which_parts:  specifies which outputs kernel(s) to use in prediction
+        :type which_parts: ('all', list of bools)
+        :param full_cov: whether to return the full covariance matrix, or just the diagonal
+        :type full_cov: bool
+        :returns: posterior mean,  a Numpy array, Nnew x self.input_dim
+        :returns: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
+        :returns: lower and upper boundaries of the 95% confidence intervals, Numpy arrays,  Nnew x self.input_dim
+
+        .. Note:: For multiple output models only
+        """
+        assert hasattr(self,'multioutput'), 'This function is for multiple output models only.'
+        index = np.ones_like(Xnew)*output
+        Xnew = np.hstack((Xnew,index))
+
+        # normalize X values
+        Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale
+        mu, var = self._raw_predict(Xnew, full_cov=full_cov, which_parts=which_parts)
+
+        # now push through likelihood
+        mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov, noise_model = output)
+        return mean, var, _025pm, _975pm
+
+    def _raw_predict_single_output(self, _Xnew, output=0, which_parts='all', full_cov=False,stop=False):
+        """
+        Internal helper function for making predictions for a specific output,
+        does not account for normalization or likelihood
+        ---------
+
+        :param Xnew: The points at which to make a prediction
+        :type Xnew: np.ndarray, Nnew x self.input_dim
+        :param output: output to predict
+        :type output: integer in {0,..., num_outputs-1}
+        :param which_parts:  specifies which outputs kernel(s) to use in prediction
+        :type which_parts: ('all', list of bools)
+        :param full_cov: whether to return the full covariance matrix, or just the diagonal
+
+        .. Note:: For multiple output models only
+        """
+        assert hasattr(self,'multioutput'), 'This function is for multiple output models only.'
+        # creates an index column and appends it to _Xnew
+        index = np.ones_like(_Xnew)*output
+        _Xnew = np.hstack((_Xnew,index))
+
+        Kx = self.kern.K(_Xnew,self.X,which_parts=which_parts).T
+        KiKx, _ = dpotrs(self.L, np.asfortranarray(Kx), lower=1)
+        mu = np.dot(KiKx.T, self.likelihood.Y)
+        if full_cov:
+            Kxx = self.kern.K(_Xnew, which_parts=which_parts)
+            var = Kxx - np.dot(KiKx.T, Kx)
+        else:
+            Kxx = self.kern.Kdiag(_Xnew, which_parts=which_parts)
+            var = Kxx - np.sum(np.multiply(KiKx, Kx), 0)
+            var = var[:, None]
+        if stop:
+            debug_this # @UndefinedVariable
+        return mu, var

GPy/core/gp_base.py

@@ -57,18 +57,12 @@ class GPBase(Model):
         self.X = state.pop()
         Model.setstate(self, state)
 
-    def plot_f(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, full_cov=False, fignum=None, ax=None):
+    def plot_f(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, full_cov=False, fignum=None, ax=None,output=None):
         """
         Plot the GP's view of the world, where the data is normalized and the
-        likelihood is Gaussian.
-
-        Plot the posterior of the GP.
           - In one dimension, the function is plotted with a shaded region identifying two standard deviations.
           - In two dimsensions, a contour-plot shows the mean predicted function
-          - In higher dimensions, we've no implemented this yet !TODO!
+          - Not implemented in higher dimensions
-
-        Can plot only part of the data and part of the posterior functions
-        using which_data and which_functions
 
         :param samples: the number of a posteriori samples to plot
         :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
@@ -85,6 +79,8 @@ class GPBase(Model):
         :param ax: axes to plot on.
         :type ax: axes handle
 
+        :param output: which output to plot (for multiple output models only)
+        :type output: integer (first output is 0)
         """
         if which_data == 'all':
             which_data = slice(None)
@@ -93,6 +89,8 @@ class GPBase(Model):
             fig = pb.figure(num=fignum)
             ax = fig.add_subplot(111)
 
+        if not hasattr(self,'multioutput'):
+
             if self.X.shape[1] == 1:
                 Xnew, xmin, xmax = x_frame1D(self.X, plot_limits=plot_limits)
                 if samples == 0:
@@ -101,16 +99,22 @@ class GPBase(Model):
                     ax.plot(self.X[which_data], self.likelihood.Y[which_data], 'kx', mew=1.5)
                 else:
                     m, v = self._raw_predict(Xnew, which_parts=which_parts, full_cov=True)
+                    v = v.reshape(m.size,-1) if len(v.shape)==3 else v
                     Ysim = np.random.multivariate_normal(m.flatten(), v, samples)
                     gpplot(Xnew, m, m - 2 * np.sqrt(np.diag(v)[:, None]), m + 2 * np.sqrt(np.diag(v))[:, None, ], axes=ax)
                     for i in range(samples):
                         ax.plot(Xnew, Ysim[i, :], Tango.colorsHex['darkBlue'], linewidth=0.25)
+
                 ax.plot(self.X[which_data], self.likelihood.Y[which_data], 'kx', mew=1.5)
                 ax.set_xlim(xmin, xmax)
                 ymin, ymax = min(np.append(self.likelihood.Y, m - 2 * np.sqrt(np.diag(v)[:, None]))), max(np.append(self.likelihood.Y, m + 2 * np.sqrt(np.diag(v)[:, None])))
                 ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
                 ax.set_ylim(ymin, ymax)
 
+                if hasattr(self,'Z'):
+                    Zu = self.Z * self._Xscale + self._Xoffset
+                    ax.plot(Zu, np.zeros_like(Zu) + ax.get_ylim()[0], 'r|', mew=1.5, markersize=12)
+
             elif self.X.shape[1] == 2:
                 resolution = resolution or 50
                 Xnew, xmin, xmax, xx, yy = x_frame2D(self.X, plot_limits, resolution)
@@ -120,17 +124,54 @@ class GPBase(Model):
                 ax.scatter(self.X[:, 0], self.X[:, 1], 40, self.likelihood.Y, linewidth=0, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max()) # @UndefinedVariable
                 ax.set_xlim(xmin[0], xmax[0])
                 ax.set_ylim(xmin[1], xmax[1])
+
+            else:
+                raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
+        else:
+            assert len(self.likelihood.noise_model_list) > output, 'The model has only %s outputs.' %self.num_outputs
+
+            if self.X.shape[1] == 2:
+                Xu = self.X[self.X[:,-1]==output ,0:1]
+                Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits)
+
+                if samples == 0:
+                    m, v = self._raw_predict_single_output(Xnew, output=output, which_parts=which_parts)
+                    gpplot(Xnew, m, m - 2 * np.sqrt(v), m + 2 * np.sqrt(v), axes=ax)
+                    ax.plot(Xu[which_data], self.likelihood.Y[self.likelihood.index==output][:,None], 'kx', mew=1.5)
+                else:
+                    m, v = self._raw_predict_single_output(Xnew, output=output, which_parts=which_parts, full_cov=True)
+                    v = v.reshape(m.size,-1) if len(v.shape)==3 else v
+                    Ysim = np.random.multivariate_normal(m.flatten(), v, samples)
+                    gpplot(Xnew, m, m - 2 * np.sqrt(np.diag(v)[:, None]), m + 2 * np.sqrt(np.diag(v))[:, None, ], axes=ax)
+                    for i in range(samples):
+                        ax.plot(Xnew, Ysim[i, :], Tango.colorsHex['darkBlue'], linewidth=0.25)
+                ax.set_xlim(xmin, xmax)
+                ymin, ymax = min(np.append(self.likelihood.Y, m - 2 * np.sqrt(np.diag(v)[:, None]))), max(np.append(self.likelihood.Y, m + 2 * np.sqrt(np.diag(v)[:, None])))
+                ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
+                ax.set_ylim(ymin, ymax)
+
+            elif self.X.shape[1] == 3:
+                raise NotImplementedError, "Plots not implemented for multioutput models with 2D inputs...yet"
+                assert self.num_outputs >= output, 'The model has only %s outputs.' %self.num_outputs
+
             else:
                 raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
 
-    def plot(self, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, samples=0, fignum=None, ax=None, fixed_inputs=[], linecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue']):
+        if hasattr(self,'Z'):
+            Zu = self.Z[self.Z[:,-1]==output,:]
+            Zu = self.Z * self._Xscale + self._Xoffset
+            Zu = self.Z[self.Z[:,-1]==output ,0:1] #??
+            ax.plot(Zu, np.zeros_like(Zu) + ax.get_ylim()[0], 'r|', mew=1.5, markersize=12)
+
+
+    def plot(self, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, samples=0, fignum=None, ax=None, output=None, fixed_inputs=[], linecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue']):
         """
         Plot the GP with noise where the likelihood is Gaussian.
 
         Plot the posterior of the GP.
           - In one dimension, the function is plotted with a shaded region identifying two standard deviations.
           - In two dimsensions, a contour-plot shows the mean predicted function
-          - In higher dimensions, we've no implemented this yet !TODO!
+          - Not implemented in higher dimensions
 
         Can plot only part of the data and part of the posterior functions
         using which_data and which_functions
@@ -151,15 +192,13 @@ class GPBase(Model):
         :type fignum: figure number
         :param ax: axes to plot on.
         :type ax: axes handle
+        :type output: integer (first output is 0)
         :param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v.
         :type fixed_inputs: a list of tuples
         :param linecol: color of line to plot.
         :type linecol:
         :param fillcol: color of fill
-        :type fillcol: 
+        :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
-        :param levels: for 2D plotting, the number of contour levels to use
-        is ax is None, create a new figure
-
         """
         # TODO include samples
         if which_data == 'all':
@@ -169,11 +208,13 @@ class GPBase(Model):
             fig = pb.figure(num=fignum)
             ax = fig.add_subplot(111)
 
+        if not hasattr(self,'multioutput'):
+
             plotdims = self.input_dim - len(fixed_inputs)
-
             if plotdims == 1:
+                resolution = resolution or 200
 
-            Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now
+                Xu = self.X * self._Xscale + self._Xoffset #NOTE self.X are the normalized values now
 
                 fixed_dims = np.array([i for i,v in fixed_inputs])
                 freedim = np.setdiff1d(np.arange(self.input_dim),fixed_dims)
@@ -193,17 +234,72 @@ class GPBase(Model):
                 ax.set_xlim(xmin, xmax)
                 ax.set_ylim(ymin, ymax)
 
-        elif self.X.shape[1] == 2: # FIXME
+
+
+                Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits,resolution=resolution)
+                m, _, lower, upper = self.predict(Xnew, which_parts=which_parts)
+                for d in range(m.shape[1]):
+                    gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax)
+                    ax.plot(Xu[which_data], self.likelihood.data[which_data, d], 'kx', mew=1.5)
+                ymin, ymax = min(np.append(self.likelihood.data, lower)), max(np.append(self.likelihood.data, upper))
+                ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
+                ax.set_xlim(xmin, xmax)
+                ax.set_ylim(ymin, ymax)
+
+            elif self.X.shape[1] == 2:
                 resolution = resolution or 50
                 Xnew, _, _, xmin, xmax = x_frame2D(self.X, plot_limits, resolution)
                 x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution)
                 m, _, lower, upper = self.predict(Xnew, which_parts=which_parts)
                 m = m.reshape(resolution, resolution).T
                 ax.contour(x, y, m, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) # @UndefinedVariable
-            Yf = self.likelihood.data.flatten()
+                Yf = self.likelihood.Y.flatten()
                 ax.scatter(self.X[:, 0], self.X[:, 1], 40, Yf, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.) # @UndefinedVariable
                 ax.set_xlim(xmin[0], xmax[0])
                 ax.set_ylim(xmin[1], xmax[1])
 
             else:
                 raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
+
+        else:
+            assert len(self.likelihood.noise_model_list) > output, 'The model has only %s outputs.' %self.num_outputs
+            if self.X.shape[1] == 2:
+                resolution = resolution or 200
+                Xu = self.X[self.X[:,-1]==output,:] #keep the output of interest
+                Xu = self.X * self._Xscale + self._Xoffset
+                Xu = self.X[self.X[:,-1]==output ,0:1] #get rid of the index column
+
+                Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits)
+                m, _, lower, upper = self.predict_single_output(Xnew, which_parts=which_parts,output=output)
+
+                for d in range(m.shape[1]):
+                    gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax)
+                    ax.plot(Xu[which_data], self.likelihood.noise_model_list[output].data, 'kx', mew=1.5)
+                ymin, ymax = min(np.append(self.likelihood.data, lower)), max(np.append(self.likelihood.data, upper))
+                ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
+                ax.set_xlim(xmin, xmax)
+                ax.set_ylim(ymin, ymax)
+
+            elif self.X.shape[1] == 3:
+                raise NotImplementedError, "Plots not yet implemented for multioutput models with 2D inputs"
+                resolution = resolution or 50
+
+            else:
+                raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
+
+    """
+    def samples_f(self,X,samples=10, which_data='all', which_parts='all',output=None):
+        if which_data == 'all':
+            which_data = slice(None)
+
+        if hasattr(self,'multioutput'):
+            np.hstack([X,np.ones((X.shape[0],1))*output])
+
+        m, v = self._raw_predict(X, which_parts=which_parts, full_cov=True)
+        v = v.reshape(m.size,-1) if len(v.shape)==3 else v
+        Ysim = np.random.multivariate_normal(m.flatten(), v, samples)
+        #gpplot(X, m, m - 2 * np.sqrt(np.diag(v)[:, None]), m + 2 * np.sqrt(np.diag(v))[:, None, ], axes=ax)
+        for i in range(samples):
+            ax.plot(X, Ysim[i, :], Tango.colorsHex['darkBlue'], linewidth=0.25)
+
+    """

GPy/core/mapping.py

@@ -49,6 +49,7 @@ class Mapping(Parameterized):
 
     def plot(self, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, samples=0, fignum=None, ax=None, fixed_inputs=[], linecol=Tango.colorsHex['darkBlue']):
         """
+
         Plot the mapping.
         
         Plots the mapping associated with the model.
@@ -79,8 +80,7 @@ class Mapping(Parameterized):
         :type fixed_inputs: a list of tuples
         :param linecol: color of line to plot.
         :type linecol:
-        :param levels: for 2D plotting, the number of contour levels to use
+        :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
-        is ax is None, create a new figure
 
         """
         # TODO include samples

GPy/core/model.py

@@ -1,4 +1,4 @@
-# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Copyright (c) 2012, 2013, GPy authors (see AUTHORS.txt).
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
 
@@ -31,8 +31,8 @@ class Model(Parameterized):
     def getstate(self):
         """
         Get the current state of the class.
-        
         Inherited from Parameterized, so add those parameters to the state
+
         :return: list of states from the model.
 
         """
@@ -47,6 +47,7 @@ class Model(Parameterized):
 
         :param state: the state of the model.
         :type state: list as returned from getstate.
+
         """
         self.preferred_optimizer = state.pop()
         self.sampling_runs = state.pop()
@@ -56,10 +57,11 @@ class Model(Parameterized):
 
     def set_prior(self, regexp, what):
         """
+
         Sets priors on the model parameters.
 
-        Notes
+        **Notes**
-        -----
+
         Asserts that the prior is suitable for the constraint. If the
         wrong constraint is in place, an error is raised.  If no
         constraint is in place, one is added (warning printed).
@@ -185,8 +187,8 @@ class Model(Parameterized):
         be handled silently.  If _all_ runs fail, the model is reset to the
         existing parameter values.
 
-        Notes
+        **Notes**
-        -----
+
         :param num_restarts: number of restarts to use (default 10)
         :type num_restarts: int
         :param robust: whether to handle exceptions silently or not (default False)
@@ -195,7 +197,9 @@ class Model(Parameterized):
         :type parallel: bool
         :param num_processes: number of workers in the multiprocessing pool
         :type numprocesses: int
-        **kwargs are passed to the optimizer. They can be:
+
+        \*\*kwargs are passed to the optimizer. They can be:
+
         :param max_f_eval: maximum number of function evaluations
         :type max_f_eval: int
         :param max_iters: maximum number of iterations
@@ -203,9 +207,7 @@ class Model(Parameterized):
         :param messages: whether to display during optimisation
         :type messages: bool
 
-        ..Note: If num_processes is None, the number of workes in the multiprocessing pool is automatically
+        .. note:: If num_processes is None, the number of workes in the multiprocessing pool is automatically set to the number of processors on the current machine.
-        set to the number of processors on the current machine.
-
 
         """
         initial_parameters = self._get_params_transformed()
@@ -397,17 +399,20 @@ class Model(Parameterized):
             return np.nan
         return 0.5 * self._get_params().size * np.log(2 * np.pi) + self.log_likelihood() - hld
 
-    def __str__(self, names=None):
+    def __str__(self):
-        if names is None:
+        s = Parameterized.__str__(self).split('\n')
-            names = self._get_print_names()
+        #def __str__(self, names=None):
-        s = Parameterized.__str__(self, names=names).split('\n')
+        #    if names is None:
+        #        names = self._get_print_names()
+        #s = Parameterized.__str__(self, names=names).split('\n')
         # add priors to the string
         if self.priors is not None:
             strs = [str(p) if p is not None else '' for p in self.priors]
         else:
-            strs = [''] * len(self._get_param_names())
+            strs = [''] * len(self._get_params())
-        name_indices = self.grep_param_names("|".join(names))
+       #         strs = [''] * len(self._get_param_names())
-        strs = np.array(strs)[name_indices]
+       #     name_indices = self.grep_param_names("|".join(names))
+       #     strs = np.array(strs)[name_indices]
         width = np.array(max([len(p) for p in strs] + [5])) + 4
 
         log_like = self.log_likelihood()
@@ -456,7 +461,7 @@ class Model(Parameterized):
             gradient = self.objective_function_gradients(x)
 
             numerical_gradient = (f1 - f2) / (2 * dx)
-            global_ratio = (f1 - f2) / (2 * np.dot(dx, gradient))
+            global_ratio = (f1 - f2) / (2 * np.dot(dx, np.where(gradient==0, 1e-32, gradient)))
 
             return (np.abs(1. - global_ratio) < tolerance) or (np.abs(gradient - numerical_gradient).mean() < tolerance)
         else:
@@ -496,7 +501,7 @@ class Model(Parameterized):
                 gradient = self.objective_function_gradients(x)[i]
 
                 numerical_gradient = (f1 - f2) / (2 * step)
-                ratio = (f1 - f2) / (2 * step * gradient)
+                ratio = (f1 - f2) / (2 * step * np.where(gradient==0, 1e-312, gradient))
                 difference = np.abs((f1 - f2) / 2 / step - gradient)
 
                 if (np.abs(1. - ratio) < tolerance) or np.abs(difference) < tolerance:
@@ -535,22 +540,17 @@ class Model(Parameterized):
             return k.variances
 
 
-    def pseudo_EM(self, epsilon=.1, **kwargs):
+    def pseudo_EM(self, stop_crit=.1, **kwargs):
         """
-        TODO: Should this not bein the GP class?
         EM - like algorithm  for Expectation Propagation and Laplace approximation
 
-        kwargs are passed to the optimize function. They can be:
+        :param stop_crit: convergence criterion
-
+        :type stop_crit: float
-        :epsilon: convergence criterion
-        :max_f_eval: maximum number of function evaluations
-        :messages: whether to display during optimisation
-        :param optimzer: whice optimizer to use (defaults to self.preferred optimizer)
-        :type optimzer: string TODO: valid strings?
 
+        .. Note: kwargs are passed to update_likelihood and optimize functions.
         """
-        assert isinstance(self.likelihood, likelihoods.EP), "pseudo_EM is only available for EP likelihoods"
+        assert isinstance(self.likelihood, (likelihoods.EP, likelihoods.EP_Mixed_Noise, likelihoods.Laplace)), "pseudo_EM is only available for approximate likelihoods"
-        ll_change = epsilon + 1.
+        ll_change = stop_crit + 1.
         iteration = 0
         last_ll = -np.inf
 
@@ -558,9 +558,24 @@ class Model(Parameterized):
         alpha = 0
         stop = False
 
+        #Handle **kwargs
+        ep_args = {}
+        for arg in kwargs.keys():
+            if arg in ('epsilon','power_ep'):
+                ep_args[arg] = kwargs[arg]
+                del kwargs[arg]
+
         while not stop:
             last_approximation = self.likelihood.copy()
             last_params = self._get_params()
+            if len(ep_args) == 2:
+                self.update_likelihood_approximation(epsilon=ep_args['epsilon'],power_ep=ep_args['power_ep'])
+            elif len(ep_args) == 1:
+                if  ep_args.keys()[0] == 'epsilon':
+                    self.update_likelihood_approximation(epsilon=ep_args['epsilon'])
+                elif ep_args.keys()[0] == 'power_ep':
+                    self.update_likelihood_approximation(power_ep=ep_args['power_ep'])
+            else:
                 self.update_likelihood_approximation()
             new_ll = self.log_likelihood()
             ll_change = new_ll - last_ll
@@ -573,7 +588,7 @@ class Model(Parameterized):
             else:
                 self.optimize(**kwargs)
                 last_ll = self.log_likelihood()
-                if ll_change < epsilon:
+                if ll_change < stop_crit:
                     stop = True
             iteration += 1
             if stop:

GPy/core/parameterized.py

@@ -27,9 +27,9 @@ class Parameterized(object):
 
     def _get_param_names(self):
         raise NotImplementedError, "this needs to be implemented to use the Parameterized class"
-    def _get_print_names(self):
+    #def _get_print_names(self):
-        """ Override for which names to print out, when using print m """
+    #    """ Override for which names to print out, when using print m """
-        return self._get_param_names()
+    #    return self._get_param_names()
 
     def pickle(self, filename, protocol=None):
         if protocol is None:
@@ -63,8 +63,8 @@ class Parameterized(object):
         """
         Get the current state of the class,
         here just all the indices, rest can get recomputed
-        
         For inheriting from Parameterized:
+
         Allways append the state of the inherited object
         and call down to the inherited object in setstate!!
         """
@@ -231,17 +231,19 @@ class Parameterized(object):
 
     def constrain_fixed(self, regexp, value=None):
         """
-        Arguments
+
-        ---------
         :param regexp: which parameters need to be fixed.
         :type regexp: ndarray(dtype=int) or regular expression object or string
         :param value: the vlaue to fix the parameters to. If the value is not specified,
                  the parameter is fixed to the current value
         :type value: float
-        Notes
+
-        -----
+        **Notes**
+
         Fixing a parameter which is tied to another, or constrained in some way will result in an error.
-        To fix multiple parameters to the same value, simply pass a regular expression which matches both parameter names, or pass both of the indexes
+
+        To fix multiple parameters to the same value, simply pass a regular expression which matches both parameter names, or pass both of the indexes.
+
         """
         matches = self.grep_param_names(regexp)
         overlap = set(matches).intersection(set(self.all_constrained_indices()))
@@ -336,26 +338,30 @@ class Parameterized(object):
         n = [nn for i, nn in enumerate(n) if not i in remove]
         return n
 
-    @property
+    #@property
-    def all(self):
+    #def all(self):
-        return self.__str__(self._get_param_names())
+    #    return self.__str__(self._get_param_names())
 
 
-    def __str__(self, names=None, nw=30):
+    #def __str__(self, names=None, nw=30):
+    def __str__(self, nw=30):
         """
         Return a string describing the parameter names and their ties and constraints
         """
-        if names is None:
+        names = self._get_param_names()
-            names = self._get_print_names()
+        #if names is None:
-        name_indices = self.grep_param_names("|".join(names))
+        #    names = self._get_print_names()
+        #name_indices = self.grep_param_names("|".join(names))
         N = len(names)
 
         if not N:
             return "This object has no free parameters."
         header = ['Name', 'Value', 'Constraints', 'Ties']
-        values = self._get_params()[name_indices] # map(str,self._get_params())
+        values = self._get_params() # map(str,self._get_params())
+        #values = self._get_params()[name_indices] # map(str,self._get_params())
         # sort out the constraints
-        constraints = [''] * len(self._get_param_names())
+        constraints = [''] * len(names)
+        #constraints = [''] * len(self._get_param_names())
         for i, t in zip(self.constrained_indices, self.constraints):
             for ii in i:
                 constraints[ii] = t.__str__()
@@ -368,6 +374,9 @@ class Parameterized(object):
             for j in tie:
                 ties[j] = '(' + str(i) + ')'
 
+        if values.size == 1:
+            values = ['%.4f' %float(values)]
+        else:
             values = ['%.4f' % float(v) for v in values]
         max_names = max([len(names[i]) for i in range(len(names))] + [len(header[0])])
         max_values = max([len(values[i]) for i in range(len(values))] + [len(header[1])])
@@ -383,3 +392,77 @@ class Parameterized(object):
 
 
         return ('\n'.join([header_string[0], separator] + param_string)) + '\n'
+
+    def grep_model(self,regexp):
+        regexp_indices = self.grep_param_names(regexp)
+        all_names = self._get_param_names()
+
+        names = [all_names[pj] for pj in regexp_indices]
+        N = len(names)
+
+        if not N:
+            return "Match not found."
+
+        header = ['Name', 'Value', 'Constraints', 'Ties']
+        all_values = self._get_params()
+        values = np.array([all_values[pj] for pj in regexp_indices])
+        constraints = [''] * len(names)
+
+        _constrained_indices,aux = self._pick_elements(regexp_indices,self.constrained_indices)
+        _constraints = [self.constraints[pj] for pj in aux]
+
+        for i, t in zip(_constrained_indices, _constraints):
+            for ii in i:
+                iii = regexp_indices.tolist().index(ii)
+                constraints[iii] = t.__str__()
+
+        _fixed_indices,aux = self._pick_elements(regexp_indices,self.fixed_indices)
+        for i in _fixed_indices:
+            for ii in i:
+                iii = regexp_indices.tolist().index(ii)
+                constraints[ii] = 'Fixed'
+
+        _tied_indices,aux = self._pick_elements(regexp_indices,self.tied_indices)
+        ties = [''] * len(names)
+        for i,ti in zip(_tied_indices,aux):
+            for ii in i:
+                iii = regexp_indices.tolist().index(ii)
+                ties[iii] = '(' + str(ti) + ')'
+
+        if values.size == 1:
+            values = ['%.4f' %float(values)]
+        else:
+            values = ['%.4f' % float(v) for v in values]
+
+        max_names = max([len(names[i]) for i in range(len(names))] + [len(header[0])])
+        max_values = max([len(values[i]) for i in range(len(values))] + [len(header[1])])
+        max_constraint = max([len(constraints[i]) for i in range(len(constraints))] + [len(header[2])])
+        max_ties = max([len(ties[i]) for i in range(len(ties))] + [len(header[3])])
+        cols = np.array([max_names, max_values, max_constraint, max_ties]) + 4
+
+        header_string = ["{h:^{col}}".format(h=header[i], col=cols[i]) for i in range(len(cols))]
+        header_string = map(lambda x: '|'.join(x), [header_string])
+        separator = '-' * len(header_string[0])
+        param_string = ["{n:^{c0}}|{v:^{c1}}|{c:^{c2}}|{t:^{c3}}".format(n=names[i], v=values[i], c=constraints[i], t=ties[i], c0=cols[0], c1=cols[1], c2=cols[2], c3=cols[3]) for i in range(len(values))]
+
+        print header_string[0]
+        print separator
+        for string in param_string:
+            print string
+
+    def _pick_elements(self,regexp_ind,array_list):
+        """Removes from array_list the elements different from regexp_ind"""
+        new_array_list = [] #New list with elements matching regexp_ind
+        array_indices = [] #Indices that matches the arrays in new_array_list and array_list
+
+        array_index = 0
+        for array in array_list:
+            _new = []
+            for ai in array:
+                if ai in regexp_ind:
+                    _new.append(ai)
+            if len(_new):
+                new_array_list.append(np.array(_new))
+                array_indices.append(array_index)
+            array_index += 1
+        return new_array_list, array_indices

GPy/core/sparse_gp.py

@@ -5,7 +5,7 @@ import numpy as np
 import pylab as pb
 from ..util.linalg import mdot, jitchol, tdot, symmetrify, backsub_both_sides, chol_inv, dtrtrs, dpotrs, dpotri
 from scipy import linalg
-from ..likelihoods import Gaussian
+from ..likelihoods import Gaussian, EP,EP_Mixed_Noise
 from gp_base import GPBase
 
 class SparseGP(GPBase):
@@ -16,16 +16,17 @@ class SparseGP(GPBase):
     :type X: np.ndarray (num_data x input_dim)
     :param likelihood: a likelihood instance, containing the observed data
     :type likelihood: GPy.likelihood.(Gaussian | EP | Laplace)
-    :param kernel : the kernel (covariance function). See link kernels
+    :param kernel: the kernel (covariance function). See link kernels
     :type kernel: a GPy.kern.kern instance
     :param X_variance: The uncertainty in the measurements of X (Gaussian variance)
     :type X_variance: np.ndarray (num_data x input_dim) | None
     :param Z: inducing inputs (optional, see note)
     :type Z: np.ndarray (num_inducing x input_dim) | None
-    :param num_inducing : Number of inducing points (optional, default 10. Ignored if Z is not None)
+    :param num_inducing: Number of inducing points (optional, default 10. Ignored if Z is not None)
     :type num_inducing: int
-    :param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
+    :param normalize_(X|Y): whether to normalize the data before computing (predictions will be in original scales)
     :type normalize_(X|Y): bool
+
     """
 
     def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
@@ -109,7 +110,6 @@ class SparseGP(GPBase):
         tmp, _ = dtrtrs(self._Lm, np.asfortranarray(tmp.T), lower=1)
         self._A = tdot(tmp)
 
-
         # factor B
         self.B = np.eye(self.num_inducing) + self._A
         self.LB = jitchol(self.B)
@@ -139,6 +139,7 @@ class SparseGP(GPBase):
         dL_dpsi2_beta = 0.5 * backsub_both_sides(self._Lm, self.output_dim * np.eye(self.num_inducing) - self.DBi_plus_BiPBi)
 
         if self.likelihood.is_heteroscedastic:
+
             if self.has_uncertain_inputs:
                 self.dL_dpsi2 = self.likelihood.precision.flatten()[:, None, None] * dL_dpsi2_beta[None, :, :]
             else:
@@ -160,9 +161,27 @@ class SparseGP(GPBase):
             # save computation here.
             self.partial_for_likelihood = None
         elif self.likelihood.is_heteroscedastic:
-            raise NotImplementedError, "heteroscedatic derivates not implemented"
+
+            if self.has_uncertain_inputs:
+                raise NotImplementedError, "heteroscedatic derivates with uncertain inputs not implemented"
+
             else:
-            # likelihood is not heterscedatic
+
+                LBi = chol_inv(self.LB)
+                Lmi_psi1, nil = dtrtrs(self._Lm, np.asfortranarray(self.psi1.T), lower=1, trans=0)
+                _LBi_Lmi_psi1, _ = dtrtrs(self.LB, np.asfortranarray(Lmi_psi1), lower=1, trans=0)
+
+
+                self.partial_for_likelihood = -0.5 * self.likelihood.precision + 0.5 * self.likelihood.V**2
+                self.partial_for_likelihood += 0.5 * self.output_dim * (self.psi0 - np.sum(Lmi_psi1**2,0))[:,None] * self.likelihood.precision**2
+
+                self.partial_for_likelihood += 0.5*np.sum(mdot(LBi.T,LBi,Lmi_psi1)*Lmi_psi1,0)[:,None]*self.likelihood.precision**2
+
+                self.partial_for_likelihood += -np.dot(self._LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T * self.likelihood.Y * self.likelihood.precision**2
+                self.partial_for_likelihood += 0.5*np.dot(self._LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T**2 * self.likelihood.precision**2
+
+        else:
+            # likelihood is not heteroscedatic
             self.partial_for_likelihood = -0.5 * self.num_data * self.output_dim * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
             self.partial_for_likelihood += 0.5 * self.output_dim * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self._A) * self.likelihood.precision)
             self.partial_for_likelihood += self.likelihood.precision * (0.5 * np.sum(self._A * self.DBi_plus_BiPBi) - self.data_fit)
@@ -194,10 +213,10 @@ class SparseGP(GPBase):
         return sum([['iip_%i_%i' % (i, j) for j in range(self.Z.shape[1])] for i in range(self.Z.shape[0])], [])\
             + self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
 
-    def _get_print_names(self):
+    #def _get_print_names(self):
-        return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
+    #    return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
 
-    def update_likelihood_approximation(self):
+    def update_likelihood_approximation(self, **kwargs):
         """
         Approximates a non-gaussian likelihood using Expectation Propagation
 
@@ -211,10 +230,10 @@ class SparseGP(GPBase):
                 Kmmi = tdot(Lmi.T)
                 diag_tr_psi2Kmmi = np.array([np.trace(psi2_Kmmi) for psi2_Kmmi in np.dot(self.psi2, Kmmi)])
 
-                self.likelihood.fit_FITC(self.Kmm, self.psi1.T, diag_tr_psi2Kmmi) # This uses the fit_FITC code, but does not perfomr a FITC-EP.#TODO solve potential confusion
+                self.likelihood.fit_FITC(self.Kmm, self.psi1.T, diag_tr_psi2Kmmi, **kwargs) # This uses the fit_FITC code, but does not perfomr a FITC-EP.#TODO solve potential confusion
                 # raise NotImplementedError, "EP approximation not implemented for uncertain inputs"
             else:
-                self.likelihood.fit_DTC(self.Kmm, self.psi1.T)
+                self.likelihood.fit_DTC(self.Kmm, self.psi1.T, **kwargs)
                 # self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
                 self._set_params(self._get_params()) # update the GP
 
@@ -240,7 +259,7 @@ class SparseGP(GPBase):
         """
         The derivative of the bound wrt the inducing inputs Z
         """
-        dL_dZ = 2.*self.kern.dK_dX(self.dL_dKmm, self.Z) # factor of two becase of vertical and horizontal 'stripes' in dKmm_dZ
+        dL_dZ = self.kern.dK_dX(self.dL_dKmm, self.Z)
         if self.has_uncertain_inputs:
             dL_dZ += self.kern.dpsi1_dZ(self.dL_dpsi1, self.Z, self.X, self.X_variance)
             dL_dZ += self.kern.dpsi2_dZ(self.dL_dpsi2, self.Z, self.X, self.X_variance)
@@ -274,7 +293,7 @@ class SparseGP(GPBase):
                 Kxx = self.kern.Kdiag(Xnew, which_parts=which_parts)
                 var = Kxx - np.sum(Kx * np.dot(Kmmi_LmiBLmi, Kx), 0)
         else:
-            # assert which_p.Tarts=='all', "swithching out parts of variational kernels is not implemented"
+            # assert which_parts=='all', "swithching out parts of variational kernels is not implemented"
             Kx = self.kern.psi1(self.Z, Xnew, X_variance_new) # , which_parts=which_parts) TODO: which_parts
             mu = np.dot(Kx, self.Cpsi1V)
             if full_cov:
@@ -288,17 +307,18 @@ class SparseGP(GPBase):
 
     def predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False):
         """
+
         Predict the function(s) at the new point(s) Xnew.
 
-        Arguments
+        **Arguments**
-        ---------
+
         :param Xnew: The points at which to make a prediction
         :type Xnew: np.ndarray, Nnew x self.input_dim
         :param X_variance_new: The uncertainty in the prediction points
         :type X_variance_new: np.ndarray, Nnew x self.input_dim
         :param which_parts:  specifies which outputs kernel(s) to use in prediction
         :type which_parts: ('all', list of bools)
-        :param full_cov: whether to return the folll covariance matrix, or just the diagonal
+        :param full_cov: whether to return the full covariance matrix, or just the diagonal
         :type full_cov: bool
         :rtype: posterior mean,  a Numpy array, Nnew x self.input_dim
         :rtype: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
@@ -322,17 +342,17 @@ class SparseGP(GPBase):
 
         return mean, var, _025pm, _975pm
 
-    def plot(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, fignum=None, ax=None):
+    def plot(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, fignum=None, ax=None, output=None):
-
         if ax is None:
             fig = pb.figure(num=fignum)
             ax = fig.add_subplot(111)
         if which_data is 'all':
             which_data = slice(None)
 
-        GPBase.plot(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, ax=ax)
+        GPBase.plot(self, samples=0, plot_limits=plot_limits, which_data='all', which_parts='all', resolution=None, levels=20, ax=ax, output=output)
+
+        if not hasattr(self,'multioutput'):
 
-        # add the inducing inputs and some errorbars
             if self.X.shape[1] == 1:
                 if self.has_uncertain_inputs:
                     Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now
@@ -345,3 +365,108 @@ class SparseGP(GPBase):
             elif self.X.shape[1] == 2:
                 Zu = self.Z * self._Xscale + self._Xoffset
                 ax.plot(Zu[:, 0], Zu[:, 1], 'wo')
+
+        else:
+            if self.X.shape[1] == 2 and hasattr(self,'multioutput'):
+                """
+                Xu = self.X[self.X[:,-1]==output,:]
+                if self.has_uncertain_inputs:
+                    Xu = self.X * self._Xscale + self._Xoffset  # NOTE self.X are the normalized values now
+
+                    Xu = self.X[self.X[:,-1]==output ,0:1] #??
+
+                    ax.errorbar(Xu[which_data, 0], self.likelihood.data[which_data, 0],
+                                xerr=2 * np.sqrt(self.X_variance[which_data, 0]),
+                                ecolor='k', fmt=None, elinewidth=.5, alpha=.5)
+
+                """
+                Zu = self.Z[self.Z[:,-1]==output,:]
+                Zu = self.Z * self._Xscale + self._Xoffset
+                Zu = self.Z[self.Z[:,-1]==output ,0:1] #??
+                ax.plot(Zu, np.zeros_like(Zu) + ax.get_ylim()[0], 'r|', mew=1.5, markersize=12)
+                #ax.set_ylim(ax.get_ylim()[0],)
+
+            else:
+                raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
+
+    def predict_single_output(self, Xnew, output=0, which_parts='all', full_cov=False):
+        """
+        For a specific output, predict the function at the new point(s) Xnew.
+
+        :param Xnew: The points at which to make a prediction
+        :type Xnew: np.ndarray, Nnew x self.input_dim
+        :param output: output to predict
+        :type output: integer in {0,..., num_outputs-1}
+        :param which_parts:  specifies which outputs kernel(s) to use in prediction
+        :type which_parts: ('all', list of bools)
+        :param full_cov: whether to return the full covariance matrix, or just the diagonal
+        :type full_cov: bool
+        :rtype: posterior mean,  a Numpy array, Nnew x self.input_dim
+        :rtype: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
+        :rtype: lower and upper boundaries of the 95% confidence intervals, Numpy arrays,  Nnew x self.input_dim
+
+        .. Note:: For multiple output models only
+        """
+
+        assert hasattr(self,'multioutput')
+        index = np.ones_like(Xnew)*output
+        Xnew = np.hstack((Xnew,index))
+
+        # normalize X values
+        Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale
+        mu, var = self._raw_predict(Xnew, full_cov=full_cov, which_parts=which_parts)
+
+        # now push through likelihood
+        mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov, noise_model = output)
+        return mean, var, _025pm, _975pm
+
+    def _raw_predict_single_output(self, _Xnew, output=0, X_variance_new=None, which_parts='all', full_cov=False,stop=False):
+        """
+        Internal helper function for making predictions for a specific output,
+        does not account for normalization or likelihood
+        ---------
+
+        :param Xnew: The points at which to make a prediction
+        :type Xnew: np.ndarray, Nnew x self.input_dim
+        :param output: output to predict
+        :type output: integer in {0,..., num_outputs-1}
+        :param which_parts:  specifies which outputs kernel(s) to use in prediction
+        :type which_parts: ('all', list of bools)
+        :param full_cov: whether to return the full covariance matrix, or just the diagonal
+
+        .. Note:: For multiple output models only
+        """
+        Bi, _ = dpotri(self.LB, lower=0)  # WTH? this lower switch should be 1, but that doesn't work!
+        symmetrify(Bi)
+        Kmmi_LmiBLmi = backsub_both_sides(self._Lm, np.eye(self.num_inducing) - Bi)
+
+        if self.Cpsi1V is None:
+            psi1V = np.dot(self.psi1.T,self.likelihood.V)
+            tmp, _ = dtrtrs(self._Lm, np.asfortranarray(psi1V), lower=1, trans=0)
+            tmp, _ = dpotrs(self.LB, tmp, lower=1)
+            self.Cpsi1V, _ = dtrtrs(self._Lm, tmp, lower=1, trans=1)
+
+        assert hasattr(self,'multioutput')
+        index = np.ones_like(_Xnew)*output
+        _Xnew = np.hstack((_Xnew,index))
+
+        if X_variance_new is None:
+            Kx = self.kern.K(self.Z, _Xnew, which_parts=which_parts)
+            mu = np.dot(Kx.T, self.Cpsi1V)
+            if full_cov:
+                Kxx = self.kern.K(_Xnew, which_parts=which_parts)
+                var = Kxx - mdot(Kx.T, Kmmi_LmiBLmi, Kx) # NOTE this won't work for plotting
+            else:
+                Kxx = self.kern.Kdiag(_Xnew, which_parts=which_parts)
+                var = Kxx - np.sum(Kx * np.dot(Kmmi_LmiBLmi, Kx), 0)
+        else:
+            Kx = self.kern.psi1(self.Z, _Xnew, X_variance_new)
+            mu = np.dot(Kx, self.Cpsi1V)
+            if full_cov:
+                raise NotImplementedError, "TODO"
+            else:
+                Kxx = self.kern.psi0(self.Z, _Xnew, X_variance_new)
+                psi2 = self.kern.psi2(self.Z, _Xnew, X_variance_new)
+                var = Kxx - np.sum(np.sum(psi2 * Kmmi_LmiBLmi[None, :, :], 1), 1)
+
+        return mu, var[:, None]

GPy/core/svigp.py

@@ -14,6 +14,7 @@ import sys
 
 class SVIGP(GPBase):
     """
+
     Stochastic Variational inference in a Gaussian Process
 
     :param X: inputs
@@ -22,25 +23,26 @@ class SVIGP(GPBase):
     :type Y: np.ndarray of observations (N x D)
     :param batchsize: the size of a h
 
-    Additional kwargs are used as for a sparse GP. They include
+    Additional kwargs are used as for a sparse GP. They include:
 
     :param q_u: canonical parameters of the distribution squasehd into a 1D array
     :type q_u: np.ndarray
-    :param M : Number of inducing points (optional, default 10. Ignored if Z is not None)
+    :param M: Number of inducing points (optional, default 10. Ignored if Z is not None)
     :type M: int
-    :param kernel : the kernel/covariance function. See link kernels
+    :param kernel: the kernel/covariance function. See link kernels
     :type kernel: a GPy kernel
     :param Z: inducing inputs (optional, see note)
     :type Z: np.ndarray (M x Q) | None
     :param X_uncertainty: The uncertainty in the measurements of X (Gaussian variance)
     :type X_uncertainty: np.ndarray (N x Q) | None
     :param Zslices: slices for the inducing inputs (see slicing TODO: link)
-    :param M : Number of inducing points (optional, default 10. Ignored if Z is not None)
+    :param M: Number of inducing points (optional, default 10. Ignored if Z is not None)
     :type M: int
-    :param beta: noise precision. TODO> ignore beta if doing EP
+    :param beta: noise precision. TODO: ignore beta if doing EP
     :type beta: float
-    :param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
+    :param normalize_(X|Y): whether to normalize the data before computing (predictions will be in original scales)
     :type normalize_(X|Y): bool
+
     """
 
 

GPy/core/transformations.py

@@ -18,9 +18,11 @@ class transformation(object):
     def gradfactor(self, f):
         """ df_dx evaluated at self.f(x)=f"""
         raise NotImplementedError
+
     def initialize(self, f):
         """ produce a sensible initial value for f(x)"""
         raise NotImplementedError
+
     def __str__(self):
         raise NotImplementedError
 
@@ -42,15 +44,13 @@ class logexp(transformation):
 class negative_logexp(transformation):
     domain = NEGATIVE
     def f(self, x):
-        return -logexp.f(x) #np.log(1. + np.exp(x))
+        return -logexp.f(x)
     def finv(self, f):
-        return logexp.finv(-f) #np.log(np.exp(-f) - 1.)
+        return logexp.finv(-f) 
     def gradfactor(self, f):
         return -logexp.gradfactor(-f)
-        #ef = np.exp(-f)
-        #return -(ef - 1.) / ef
     def initialize(self, f):
-        return -logexp.initialize(f) #np.abs(f)
+        return -logexp.initialize(f)
     def __str__(self):
         return '(-ve)'
 
@@ -82,7 +82,6 @@ class logexp_clipped(logexp):
         return '(+ve_c)'
 
 class exponent(transformation):
-    # TODO: can't allow this to go to zero, need to set a lower bound. Similar with negative exponent below. See old MATLAB code.
     domain = POSITIVE
     def f(self, x):
         return np.where(x<lim_val, np.where(x>-lim_val, np.exp(x), np.exp(-lim_val)), np.exp(lim_val))

GPy/examples/classification.py

@@ -10,31 +10,11 @@ import numpy as np
 import GPy
 
 default_seed = 10000
-def crescent_data(seed=default_seed, kernel=None): # FIXME
-    """Run a Gaussian process classification on the crescent data. The demonstration calls the basic GP classification model and uses EP to approximate the likelihood.
-
-    :param model_type: type of model to fit ['Full', 'FITC', 'DTC'].
-    :param seed : seed value for data generation.
-    :type seed: int
-    :param inducing : number of inducing variables (only used for 'FITC' or 'DTC').
-    :type inducing: int
-    """
-
-    data = GPy.util.datasets.crescent_data(seed=seed)
-    Y = data['Y']
-    Y[Y.flatten()==-1] = 0
-
-    m = GPy.models.GPClassification(data['X'], Y)
-    #m.update_likelihood_approximation()
-    #m.optimize()
-    m.pseudo_EM()
-    print(m)
-    m.plot()
-    return m
 
 def oil(num_inducing=50, max_iters=100, kernel=None):
     """
     Run a Gaussian process classification on the three phase oil data. The demonstration calls the basic GP classification model and uses EP to approximate the likelihood.
+
     """
     data = GPy.util.datasets.oil()
     X = data['X']
@@ -64,8 +44,10 @@ def oil(num_inducing=50, max_iters=100, kernel=None):
 def toy_linear_1d_classification(seed=default_seed):
     """
     Simple 1D classification example
-    :param seed : seed value for data generation (default is 4).
+
+    :param seed: seed value for data generation (default is 4).
     :type seed: int
+
     """
 
     data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
@@ -92,8 +74,10 @@ def toy_linear_1d_classification(seed=default_seed):
 def sparse_toy_linear_1d_classification(num_inducing=10,seed=default_seed):
     """
     Sparse 1D classification example
-    :param seed : seed value for data generation (default is 4).
+
+    :param seed: seed value for data generation (default is 4).
     :type seed: int
+
     """
 
     data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
@@ -118,51 +102,67 @@ def sparse_toy_linear_1d_classification(num_inducing=10,seed=default_seed):
 
     return m
 
-def sparse_crescent_data(num_inducing=10, seed=default_seed, kernel=None):
+def toy_heaviside(seed=default_seed):
     """
-    Run a Gaussian process classification with DTC approxiamtion on the crescent data. The demonstration calls the basic GP classification model and uses EP to approximate the likelihood.
+    Simple 1D classification example using a heavy side gp transformation
+
+    :param seed: seed value for data generation (default is 4).
+    :type seed: int
+
+    """
+
+    data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
+    Y = data['Y'][:, 0:1]
+    Y[Y.flatten() == -1] = 0
+
+    # Model definition
+    noise_model = GPy.likelihoods.binomial(GPy.likelihoods.noise_models.gp_transformations.Heaviside())
+    likelihood = GPy.likelihoods.EP(Y,noise_model)
+    m = GPy.models.GPClassification(data['X'], likelihood=likelihood)
+
+    # Optimize
+    m.update_likelihood_approximation()
+    # Parameters optimization:
+    m.optimize()
+    #m.pseudo_EM()
+
+    # Plot
+    fig, axes = pb.subplots(2,1)
+    m.plot_f(ax=axes[0])
+    m.plot(ax=axes[1])
+    print(m)
+
+    return m
+
+def crescent_data(model_type='Full', num_inducing=10, seed=default_seed, kernel=None):
+    """
+    Run a Gaussian process classification on the crescent data. The demonstration calls the basic GP classification model and uses EP to approximate the likelihood.
 
     :param model_type: type of model to fit ['Full', 'FITC', 'DTC'].
-    :param seed : seed value for data generation.
+    :param inducing: number of inducing variables (only used for 'FITC' or 'DTC').
-    :type seed: int
-    :param inducing : number of inducing variables (only used for 'FITC' or 'DTC').
     :type inducing: int
+    :param seed: seed value for data generation.
+    :type seed: int
+    :param kernel: kernel to use in the model
+    :type kernel: a GPy kernel
     """
-
     data = GPy.util.datasets.crescent_data(seed=seed)
     Y = data['Y']
-    Y[Y.flatten()==-1]=0
+    Y[Y.flatten()==-1] = 0
 
+    if model_type == 'Full':
+        m = GPy.models.GPClassification(data['X'], Y,kernel=kernel)
+
+    elif model_type == 'DTC':
         m = GPy.models.SparseGPClassification(data['X'], Y, kernel=kernel, num_inducing=num_inducing)
         m['.*len'] = 10.
-    #m.update_likelihood_approximation()
-    #m.optimize()
-    m.pseudo_EM()
-    print(m)
-    m.plot()
-    return m
 
-def FITC_crescent_data(num_inducing=10, seed=default_seed):
+    elif model_type == 'FITC':
-    """
+        m = GPy.models.FITCClassification(data['X'], Y, kernel=kernel, num_inducing=num_inducing)
-    Run a Gaussian process classification with FITC approximation on the crescent data. The demonstration uses EP to approximate the likelihood.
-
-    :param model_type: type of model to fit ['Full', 'FITC', 'DTC'].
-    :param seed : seed value for data generation.
-    :type seed: int
-    :param inducing : number of inducing variables (only used for 'FITC' or 'DTC').
-    :type num_inducing: int
-    """
-
-    data = GPy.util.datasets.crescent_data(seed=seed)
-    Y = data['Y']
-    Y[Y.flatten()==-1]=0
-
-    m = GPy.models.FITCClassification(data['X'], Y,num_inducing=num_inducing)
-    m.constrain_bounded('.*len',1.,1e3)
         m['.*len'] = 3.
-    #m.update_likelihood_approximation()
+
-    #m.optimize()
     m.pseudo_EM()
     print(m)
     m.plot()
+
     return m

GPy/examples/laplace_approximations.py

@@ -26,7 +26,7 @@ def timing():
         edited_real_sd = real_sd
         kernel1 = GPy.kern.rbf(X.shape[1])
 
-        t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=edited_real_sd)
+        t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=edited_real_sd)
         corrupt_stu_t_likelihood = GPy.likelihoods.Laplace(Yc.copy(), t_distribution, opt='rasm')
         m = GPy.models.GPRegression(X, Yc.copy(), kernel1, likelihood=corrupt_stu_t_likelihood)
         m.ensure_default_constraints()
@@ -55,7 +55,7 @@ def v_fail_test():
     edited_real_sd = real_sd
 
     print "Clean student t, rasm"
-    t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=edited_real_sd)
+    t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=edited_real_sd)
     stu_t_likelihood = GPy.likelihoods.Laplace(Y.copy(), t_distribution, opt='rasm')
     m = GPy.models.GPRegression(X, Y.copy(), kernel1, likelihood=stu_t_likelihood)
     m.constrain_positive('')
@@ -102,7 +102,7 @@ def student_t_obj_plane():
     print mgp
 
     kernelst = kernelgp.copy()
-    t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=(real_std**2))
+    t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=(real_std**2))
     stu_t_likelihood = GPy.likelihoods.Laplace(Y.copy(), t_distribution, opt='rasm')
     m = GPy.models.GPRegression(X, Y, kernelst, likelihood=stu_t_likelihood)
     m.ensure_default_constraints()
@@ -155,7 +155,7 @@ def student_t_f_check():
 
     kernelst = kernelgp.copy()
     #kernelst += GPy.kern.bias(X.shape[1])
-    t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=0.05)
+    t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=0.05)
     stu_t_likelihood = GPy.likelihoods.Laplace(Y.copy(), t_distribution, opt='rasm')
     m = GPy.models.GPRegression(X, Y.copy(), kernelst, likelihood=stu_t_likelihood)
     #m['rbf_v'] = mgp._get_params()[0]
@@ -207,7 +207,7 @@ def student_t_fix_optimise_check():
     kernelst = kernelgp.copy()
     real_stu_t_std2 = (real_std**2)*((deg_free - 2)/float(deg_free))
 
-    t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=real_stu_t_std2)
+    t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=real_stu_t_std2)
     stu_t_likelihood = GPy.likelihoods.Laplace(Y.copy(), t_distribution, opt='rasm')
 
     plt.figure(1)
@@ -350,7 +350,7 @@ def debug_student_t_noise_approx():
     #edited_real_sd = real_sd
 
     print "Clean student t, rasm"
-    t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=edited_real_sd)
+    t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=edited_real_sd)
     stu_t_likelihood = GPy.likelihoods.Laplace(Y.copy(), t_distribution, opt='rasm')
 
     m = GPy.models.GPRegression(X, Y, kernel6, likelihood=stu_t_likelihood)
@@ -385,7 +385,7 @@ def debug_student_t_noise_approx():
     return m
 
     #print "Clean student t, ncg"
-    #t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=edited_real_sd)
+    #t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=edited_real_sd)
     #stu_t_likelihood = GPy.likelihoods.Laplace(Y, t_distribution, opt='ncg')
     #m = GPy.models.GPRegression(X, stu_t_likelihood, kernel3)
     #m.ensure_default_constraints()
@@ -446,7 +446,7 @@ def student_t_approx():
     plt.figure(1)
     plt.suptitle('Gaussian likelihood')
     # Kernel object
-    kernel1 = GPy.kern.rbf(X.shape[1])
+    kernel1 = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
     kernel2 = kernel1.copy()
     kernel3 = kernel1.copy()
     kernel4 = kernel1.copy()
@@ -487,13 +487,12 @@ def student_t_approx():
     edited_real_sd = initial_var_guess
 
     print "Clean student t, rasm"
-    t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=edited_real_sd)
+    t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=edited_real_sd)
     stu_t_likelihood = GPy.likelihoods.Laplace(Y.copy(), t_distribution, opt='rasm')
     m = GPy.models.GPRegression(X, Y.copy(), kernel6, likelihood=stu_t_likelihood)
     m.ensure_default_constraints()
     m.constrain_positive('t_noise')
     m.randomize()
-    import ipdb; ipdb.set_trace()  # XXX BREAKPOINT
     #m.update_likelihood_approximation()
     m.optimize()
     print(m)
@@ -504,15 +503,19 @@ def student_t_approx():
     plt.title('Student-t rasm clean')
 
     print "Corrupt student t, rasm"
-    t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=edited_real_sd)
+    t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=edited_real_sd)
     corrupt_stu_t_likelihood = GPy.likelihoods.Laplace(Yc.copy(), t_distribution, opt='rasm')
     m = GPy.models.GPRegression(X, Yc.copy(), kernel4, likelihood=corrupt_stu_t_likelihood)
     m.ensure_default_constraints()
     m.constrain_positive('t_noise')
+    m.constrain_fixed('white', 1e-4)
     m.randomize()
     #m.update_likelihood_approximation()
-    import ipdb; ipdb.set_trace()  # XXX BREAKPOINT
+    for a in range(1):
-    m.optimize()
+        m.randomize()
+        m_start = m.copy()
+        print m
+        m.optimize('scg', messages=1)
     print(m)
     ax = plt.subplot(212)
     m.plot(ax=ax)
@@ -524,7 +527,7 @@ def student_t_approx():
     return m
 
     #print "Clean student t, ncg"
-    #t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=edited_real_sd)
+    #t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=edited_real_sd)
     #stu_t_likelihood = GPy.likelihoods.Laplace(Y, t_distribution, opt='ncg')
     #m = GPy.models.GPRegression(X, Y, kernel3, likelihood=stu_t_likelihood)
     #m.ensure_default_constraints()
@@ -538,7 +541,7 @@ def student_t_approx():
     #plt.title('Student-t ncg clean')
 
     #print "Corrupt student t, ncg"
-    #t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=edited_real_sd)
+    #t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=edited_real_sd)
     #corrupt_stu_t_likelihood = GPy.likelihoods.Laplace(Yc.copy(), t_distribution, opt='ncg')
     #m = GPy.models.GPRegression(X, Y, kernel5, likelihood=corrupt_stu_t_likelihood)
     #m.ensure_default_constraints()
@@ -553,7 +556,7 @@ def student_t_approx():
 
 
     ###with a student t distribution, since it has heavy tails it should work well
-    ###likelihood_function = student_t(deg_free, sigma2=real_var)
+    ###likelihood_function = student_t(deg_free=deg_free, sigma2=real_var)
     ###lap = Laplace(Y, likelihood_function)
     ###cov = kernel.K(X)
     ###lap.fit_full(cov)
@@ -621,7 +624,7 @@ def gaussian_f_check():
     kernelg = kernelgp.copy()
     #kernelst += GPy.kern.bias(X.shape[1])
     N, D = X.shape
-    g_distribution = GPy.likelihoods.functions.Gaussian(variance=0.1, N=N, D=D)
+    g_distribution = GPy.likelihoods.noise_model_constructors.gaussian(variance=0.1, N=N, D=D)
     g_likelihood = GPy.likelihoods.Laplace(Y.copy(), g_distribution, opt='rasm')
     m = GPy.models.GPRegression(X, Y, kernelg, likelihood=g_likelihood)
     m.likelihood.X = X
@@ -698,7 +701,7 @@ def boston_example():
         print "Gaussian Laplace GP"
         kernelstu = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
         N, D = Y_train.shape
-        g_distribution = GPy.likelihoods.functions.Gaussian(variance=noise, N=N, D=D)
+        g_distribution = GPy.likelihoods.noise_model_constructors.gaussian(variance=noise, N=N, D=D)
         g_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), g_distribution, opt='rasm')
         mg = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu, likelihood=g_likelihood)
         mg.ensure_default_constraints()
@@ -725,7 +728,7 @@ def boston_example():
         deg_free = 1
         print "Student-T GP {}df".format(deg_free)
         kernelstu = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
-        t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=noise)
+        t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=noise)
         stu_t_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), t_distribution, opt='rasm')
         mstu_t = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu, likelihood=stu_t_likelihood)
         mstu_t.ensure_default_constraints()
@@ -751,7 +754,7 @@ def boston_example():
         deg_free = 2
         print "Student-T GP {}df".format(deg_free)
         kernelstu = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
-        t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=noise)
+        t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=noise)
         stu_t_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), t_distribution, opt='rasm')
         mstu_t = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu, likelihood=stu_t_likelihood)
         mstu_t.ensure_default_constraints()
@@ -778,7 +781,7 @@ def boston_example():
         deg_free = 3
         print "Student-T GP {}df".format(deg_free)
         kernelstu = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
-        t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=noise)
+        t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=noise)
         stu_t_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), t_distribution, opt='rasm')
         mstu_t = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu, likelihood=stu_t_likelihood)
         mstu_t.ensure_default_constraints()
@@ -804,7 +807,7 @@ def boston_example():
         deg_free = 5
         print "Student-T GP {}df".format(deg_free)
         kernelstu = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
-        t_distribution = GPy.likelihoods.functions.StudentT(deg_free, sigma2=noise)
+        t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=noise)
         stu_t_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), t_distribution, opt='rasm')
         mstu_t = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu, likelihood=stu_t_likelihood)
         mstu_t.ensure_default_constraints()

GPy/examples/regression.py

@@ -9,9 +9,9 @@ import pylab as pb
 import numpy as np
 import GPy
 
-def coregionalisation_toy2(max_iters=100):
+def coregionalization_toy2(max_iters=100):
     """
-    A simple demonstration of coregionalisation on two sinusoidal functions.
+    A simple demonstration of coregionalization on two sinusoidal functions.
     """
     X1 = np.random.rand(50, 1) * 8
     X2 = np.random.rand(30, 1) * 5
@@ -22,8 +22,8 @@ def coregionalisation_toy2(max_iters=100):
     Y = np.vstack((Y1, Y2))
 
     k1 = GPy.kern.rbf(1) + GPy.kern.bias(1)
-    k2 = GPy.kern.coregionalise(2, 1)
+    k2 = GPy.kern.coregionalize(2,1)
-    k = k1**k2
+    k = k1**k2 #k = k1.prod(k2,tensor=True)
     m = GPy.models.GPRegression(X, Y, kernel=k)
     m.constrain_fixed('.*rbf_var', 1.)
     # m.constrain_positive('.*kappa')
@@ -40,41 +40,32 @@ def coregionalisation_toy2(max_iters=100):
     pb.plot(X2[:, 0], Y2[:, 0], 'gx', mew=2)
     return m
 
-def coregionalisation_toy(max_iters=100):
+def coregionalization_toy(max_iters=100):
     """
-    A simple demonstration of coregionalisation on two sinusoidal functions.
+    A simple demonstration of coregionalization on two sinusoidal functions.
     """
     X1 = np.random.rand(50, 1) * 8
     X2 = np.random.rand(30, 1) * 5
-    index = np.vstack((np.zeros_like(X1), np.ones_like(X2)))
+    X = np.vstack((X1, X2))
-    X = np.hstack((np.vstack((X1, X2)), index))
     Y1 = np.sin(X1) + np.random.randn(*X1.shape) * 0.05
     Y2 = -np.sin(X2) + np.random.randn(*X2.shape) * 0.05
     Y = np.vstack((Y1, Y2))
 
     k1 = GPy.kern.rbf(1)
-    k2 = GPy.kern.coregionalise(2, 2)
+    m = GPy.models.GPMultioutputRegression(X_list=[X1,X2],Y_list=[Y1,Y2],kernel_list=[k1])
-    k = k1**k2 #k1.prod(k2, tensor=True)
-    m = GPy.models.GPRegression(X, Y, kernel=k)
     m.constrain_fixed('.*rbf_var', 1.)
-    # m.constrain_positive('kappa')
     m.optimize(max_iters=max_iters)
 
-    pb.figure()
+    fig, axes = pb.subplots(2,1)
-    Xtest1 = np.hstack((np.linspace(0, 9, 100)[:, None], np.zeros((100, 1))))
+    m.plot(output=0,ax=axes[0])
-    Xtest2 = np.hstack((np.linspace(0, 9, 100)[:, None], np.ones((100, 1))))
+    m.plot(output=1,ax=axes[1])
-    mean, var, low, up = m.predict(Xtest1)
+    axes[0].set_title('Output 0')
-    GPy.util.plot.gpplot(Xtest1[:, 0], mean, low, up)
+    axes[1].set_title('Output 1')
-    mean, var, low, up = m.predict(Xtest2)
-    GPy.util.plot.gpplot(Xtest2[:, 0], mean, low, up)
-    pb.plot(X1[:, 0], Y1[:, 0], 'rx', mew=2)
-    pb.plot(X2[:, 0], Y2[:, 0], 'gx', mew=2)
     return m
 
-
+def coregionalization_sparse(max_iters=100):
-def coregionalisation_sparse(max_iters=100):
     """
-    A simple demonstration of coregionalisation on two sinusoidal functions using sparse approximations.
+    A simple demonstration of coregionalization on two sinusoidal functions using sparse approximations.
     """
     X1 = np.random.rand(500, 1) * 8
     X2 = np.random.rand(300, 1) * 5
@@ -84,33 +75,18 @@ def coregionalisation_sparse(max_iters=100):
     Y2 = -np.sin(X2) + np.random.randn(*X2.shape) * 0.05
     Y = np.vstack((Y1, Y2))
 
-    num_inducing = 40
-    Z = np.hstack((np.random.rand(num_inducing, 1) * 8, np.random.randint(0, 2, num_inducing)[:, None]))
-
     k1 = GPy.kern.rbf(1)
-    k2 = GPy.kern.coregionalise(2, 2)
-    k = k1**k2 #.prod(k2, tensor=True) # + GPy.kern.white(2,0.001)
 
-    m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z)
+    m = GPy.models.SparseGPMultioutputRegression(X_list=[X1,X2],Y_list=[Y1,Y2],kernel_list=[k1],num_inducing=20)
-    m.constrain_fixed('.*rbf_var', 1.)
+    m.constrain_fixed('.*rbf_var',1.)
-    m.constrain_fixed('iip')
+    m.optimize(messages=1)
-    m.constrain_bounded('noise_variance', 1e-3, 1e-1)
+    #m.optimize_restarts(5, robust=True, messages=1, max_iters=max_iters, optimizer='bfgs')
-#     m.optimize_restarts(5, robust=True, messages=1, max_iters=max_iters, optimizer='bfgs')
-    m.optimize(max_iters=max_iters)
 
-    # plotting:
+    fig, axes = pb.subplots(2,1)
-    pb.figure()
+    m.plot(output=0,ax=axes[0])
-    Xtest1 = np.hstack((np.linspace(0, 9, 100)[:, None], np.zeros((100, 1))))
+    m.plot(output=1,ax=axes[1])
-    Xtest2 = np.hstack((np.linspace(0, 9, 100)[:, None], np.ones((100, 1))))
+    axes[0].set_title('Output 0')
-    mean, var, low, up = m.predict(Xtest1)
+    axes[1].set_title('Output 1')
-    GPy.util.plot.gpplot(Xtest1[:, 0], mean, low, up)
-    mean, var, low, up = m.predict(Xtest2)
-    GPy.util.plot.gpplot(Xtest2[:, 0], mean, low, up)
-    pb.plot(X1[:, 0], Y1[:, 0], 'rx', mew=2)
-    pb.plot(X2[:, 0], Y2[:, 0], 'gx', mew=2)
-    y = pb.ylim()[0]
-    pb.plot(Z[:, 0][Z[:, 1] == 0], np.zeros(np.sum(Z[:, 1] == 0)) + y, 'r|', mew=2)
-    pb.plot(Z[:, 0][Z[:, 1] == 1], np.zeros(np.sum(Z[:, 1] == 1)) + y, 'g|', mew=2)
     return m
 
 def epomeo_gpx(max_iters=100):
@@ -136,7 +112,7 @@ def epomeo_gpx(max_iters=100):
                    np.random.randint(0, 4, num_inducing)[:, None]))
 
     k1 = GPy.kern.rbf(1)
-    k2 = GPy.kern.coregionalise(output_dim=5, rank=5)
+    k2 = GPy.kern.coregionalize(output_dim=5, rank=5)
     k = k1**k2
 
     m = GPy.models.SparseGPRegression(t, Y, kernel=k, Z=Z, normalize_Y=True)
@@ -156,7 +132,7 @@ def multiple_optima(gene_number=937, resolution=80, model_restarts=10, seed=1000
     length_scales = np.linspace(0.1, 60., resolution)
     log_SNRs = np.linspace(-3., 4., resolution)
 
-    data = GPy.util.datasets.della_gatta_TRP63_gene_expression(gene_number)
+    data = GPy.util.datasets.della_gatta_TRP63_gene_expression(data_set='della_gatta',gene_number=gene_number)
     # data['Y'] = data['Y'][0::2, :]
     # data['X'] = data['X'][0::2, :]
 
@@ -401,8 +377,6 @@ def silhouette(max_iters=100):
     print(m)
     return m
 
-
-
 def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100):
     """Run a 1D example of a sparse GP regression."""
     # sample inputs and outputs

GPy/inference/conjugate_gradient_descent.py

@@ -233,7 +233,7 @@ class CGD(Async_Optimize):
         """
         opt_async(self, f, df, x0, callback, update_rule=FletcherReeves,
                messages=0, maxiter=5e3, max_f_eval=15e3, gtol=1e-6,
-               report_every=10, *args, **kwargs)
+               report_every=10, \*args, \*\*kwargs)
         
         callback gets called every `report_every` iterations
 
@@ -244,16 +244,14 @@ class CGD(Async_Optimize):
     
         f, and df will be called with
             
-            f(xi, *args, **kwargs)
+            f(xi, \*args, \*\*kwargs)
-            df(xi, *args, **kwargs)
+            df(xi, \*args, \*\*kwargs)
         
-        **returns**
+        **Returns:**
-        -----------
         
             Started `Process` object, optimizing asynchronously 
         
-        **calls** 
+        **Calls:** 
-        ---------
         
             callback(x_opt, f_opt, g_opt, iteration, function_calls, gradient_calls, status_message)
         
@@ -265,7 +263,7 @@ class CGD(Async_Optimize):
         """
         opt(self, f, df, x0, callback=None, update_rule=FletcherReeves,
                messages=0, maxiter=5e3, max_f_eval=15e3, gtol=1e-6,
-               report_every=10, *args, **kwargs)
+               report_every=10, \*args, \*\*kwargs)
         
         Minimize f, calling callback every `report_every` iterations with following syntax:
         
@@ -276,11 +274,10 @@ class CGD(Async_Optimize):
     
         f, and df will be called with
             
-            f(xi, *args, **kwargs)
+            f(xi, \*args, \*\*kwargs)
-            df(xi, *args, **kwargs)
+            df(xi, \*args, \*\*kwargs)
                 
         **returns** 
-        ---------
         
             x_opt, f_opt, g_opt, iteration, function_calls, gradient_calls, status_message
         

GPy/inference/optimization.py

@@ -29,7 +29,7 @@ class Optimizer():
 
     """
     def __init__(self, x_init, messages=False, model=None, max_f_eval=1e4, max_iters=1e3,
-                 ftol=None, gtol=None, xtol=None):
+                 ftol=None, gtol=None, xtol=None, bfgs_factor=None):
         self.opt_name = None
         self.x_init = x_init
         self.messages = messages
@@ -39,6 +39,7 @@ class Optimizer():
         self.status = None
         self.max_f_eval = int(max_f_eval)
         self.max_iters = int(max_iters)
+        self.bfgs_factor = bfgs_factor
         self.trace = None
         self.time = "Not available"
         self.xtol = xtol
@@ -128,9 +129,11 @@ class opt_lbfgsb(Optimizer):
             print "WARNING: l-bfgs-b doesn't have an ftol arg, so I'm going to ignore it"
         if self.gtol is not None:
             opt_dict['pgtol'] = self.gtol
+        if self.bfgs_factor is not None:
+            opt_dict['factr'] = self.bfgs_factor
 
         opt_result = optimize.fmin_l_bfgs_b(f_fp, self.x_init, iprint=iprint,
-                                            maxfun=self.max_f_eval, **opt_dict)
+                                            maxfun=self.max_iters, **opt_dict)
         self.x_opt = opt_result[0]
         self.f_opt = f_fp(self.x_opt)[0]
         self.funct_eval = opt_result[2]['funcalls']

GPy/inference/sgd.py

@@ -10,11 +10,10 @@ class opt_SGD(Optimizer):
     """
     Optimize using stochastic gradient descent.
 
-    *** Parameters ***
+    :param Model: reference to the Model object
-    Model: reference to the Model object
+    :param iterations: number of iterations
-    iterations: number of iterations
+    :param learning_rate: learning rate
-    learning_rate: learning rate
+    :param momentum: momentum
-    momentum: momentum
 
     """
 

GPy/kern/constructors.py

@@ -5,7 +5,6 @@ import numpy as np
 from kern import kern
 import parts
 
-
 def rbf_inv(input_dim,variance=1., inv_lengthscale=None,ARD=False):
     """
     Construct an RBF kernel
@@ -18,6 +17,7 @@ def rbf_inv(input_dim,variance=1., inv_lengthscale=None,ARD=False):
     :type lengthscale: float
     :param ARD: Auto Relevance Determination (one lengthscale per dimension)
     :type ARD: Boolean
+
     """
     part = parts.rbf_inv.RBFInv(input_dim,variance,inv_lengthscale,ARD)
     return kern(input_dim, [part])
@@ -34,6 +34,7 @@ def rbf(input_dim,variance=1., lengthscale=None,ARD=False):
     :type lengthscale: float
     :param ARD: Auto Relevance Determination (one lengthscale per dimension)
     :type ARD: Boolean
+
     """
     part = parts.rbf.RBF(input_dim,variance,lengthscale,ARD)
     return kern(input_dim, [part])
@@ -42,11 +43,13 @@ def linear(input_dim,variances=None,ARD=False):
     """
      Construct a linear kernel.
 
-     Arguments
+    :param input_dim: dimensionality of the kernel, obligatory
-     ---------
+    :type input_dim: int
-    input_dimD (int), obligatory
+    :param variances:
-     variances (np.ndarray)
+    :type variances: np.ndarray
-     ARD (boolean)
+    :param ARD: Auto Relevance Determination (one lengthscale per dimension)
+    :type ARD: Boolean
+
     """
     part = parts.linear.Linear(input_dim,variances,ARD)
     return kern(input_dim, [part])
@@ -65,37 +68,40 @@ def mlp(input_dim,variance=1., weight_variance=None,bias_variance=100.,ARD=False
     :type bias_variance: float
     :param ARD: Auto Relevance Determination (allows for ARD version of covariance)
     :type ARD: Boolean
+
     """
     part = parts.mlp.MLP(input_dim,variance,weight_variance,bias_variance,ARD)
     return kern(input_dim, [part])
 
 def gibbs(input_dim,variance=1., mapping=None):
     """
+
     Gibbs and MacKay non-stationary covariance function.
 
     .. math::
 
-       r = sqrt((x_i - x_j)'*(x_i - x_j))
+       r = \\sqrt{((x_i - x_j)'*(x_i - x_j))}
 
-       k(x_i, x_j) = \sigma^2*Z*exp(-r^2/(l(x)*l(x) + l(x')*l(x')))
+       k(x_i, x_j) = \\sigma^2*Z*exp(-r^2/(l(x)*l(x) + l(x')*l(x')))
 
-       Z = \sqrt{2*l(x)*l(x')/(l(x)*l(x) + l(x')*l(x')}
+       Z = \\sqrt{2*l(x)*l(x')/(l(x)*l(x) + l(x')*l(x')}
+
+    Where :math:`l(x)` is a function giving the length scale as a function of space.
 
-       where :math:`l(x)` is a function giving the length scale as a function of space.
     This is the non stationary kernel proposed by Mark Gibbs in his 1997
     thesis. It is similar to an RBF but has a length scale that varies
     with input location. This leads to an additional term in front of
     the kernel.
 
-        The parameters are :math:`\sigma^2`, the process variance, and the parameters of l(x) which is a function that can be specified by the user, by default an multi-layer peceptron is used is used.
+    The parameters are :math:`\\sigma^2`, the process variance, and the parameters of l(x) which is a function that can be specified by the user, by default an multi-layer peceptron is used is used.
 
     :param input_dim: the number of input dimensions
     :type input_dim: int
-        :param variance: the variance :math:`\sigma^2`
+    :param variance: the variance :math:`\\sigma^2`
     :type variance: float
     :param mapping: the mapping that gives the lengthscale across the input space.
     :type mapping: GPy.core.Mapping
-        :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter \sigma^2_w), otherwise there is one weight variance parameter per dimension.
+    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter :math:`\\sigma^2_w`), otherwise there is one weight variance parameter per dimension.
     :type ARD: Boolean
     :rtype: Kernpart object
 
@@ -103,6 +109,12 @@ def gibbs(input_dim,variance=1., mapping=None):
     part = parts.gibbs.Gibbs(input_dim,variance,mapping)
     return kern(input_dim, [part])
 
+def hetero(input_dim, mapping=None, transform=None):
+    """
+    """
+    part = parts.hetero.Hetero(input_dim,mapping,transform)
+    return kern(input_dim, [part])
+
 def poly(input_dim,variance=1., weight_variance=None,bias_variance=1.,degree=2, ARD=False):
     """
     Construct a polynomial kernel
@@ -119,6 +131,7 @@ def poly(input_dim,variance=1., weight_variance=None,bias_variance=1.,degree=2,
     :type degree: int
     :param ARD: Auto Relevance Determination (allows for ARD version of covariance)
     :type ARD: Boolean
+
     """
     part = parts.poly.POLY(input_dim,variance,weight_variance,bias_variance,degree,ARD)
     return kern(input_dim, [part])
@@ -127,14 +140,43 @@ def white(input_dim,variance=1.):
     """
      Construct a white kernel.
 
-     Arguments
+    :param input_dim: dimensionality of the kernel, obligatory
-     ---------
+    :type input_dim: int
-    input_dimD (int), obligatory
+    :param variance: the variance of the kernel
-     variance (float)
+    :type variance: float
+
     """
     part = parts.white.White(input_dim,variance)
     return kern(input_dim, [part])
 
+def eq_ode1(output_dim, W=None, rank=1,  kappa=None, length_scale=1., decay=None, delay=None):
+    """Covariance function for first order differential equation driven by an exponentiated quadratic covariance.
+
+    This outputs of this kernel have the form
+    .. math::
+       \frac{\text{d}y_j}{\text{d}t} = \sum_{i=1}^R w_{j,i} f_i(t-\delta_j) +\sqrt{\kappa_j}g_j(t) - d_jy_j(t)
+
+    where :math:`R` is the rank of the system, :math:`w_{j,i}` is the sensitivity of the :math:`j`th output to the :math:`i`th latent function, :math:`d_j` is the decay rate of the :math:`j`th output and :math:`f_i(t)` and :math:`g_i(t)` are independent latent Gaussian processes goverened by an exponentiated quadratic covariance.
+    
+    :param output_dim: number of outputs driven by latent function.
+    :type output_dim: int
+    :param W: sensitivities of each output to the latent driving function. 
+    :type W: ndarray (output_dim x rank).
+    :param rank: If rank is greater than 1 then there are assumed to be a total of rank latent forces independently driving the system, each with identical covariance.
+    :type rank: int
+    :param decay: decay rates for the first order system. 
+    :type decay: array of length output_dim.
+    :param delay: delay between latent force and output response.
+    :type delay: array of length output_dim.
+    :param kappa: diagonal term that allows each latent output to have an independent component to the response.
+    :type kappa: array of length output_dim.
+    
+    .. Note: see first order differential equation examples in GPy.examples.regression for some usage.
+    """
+    part = parts.eq_ode1.Eq_ode1(output_dim, W, rank, kappa, length_scale, decay, delay)
+    return kern(2, [part])
+
+
 def exponential(input_dim,variance=1., lengthscale=None, ARD=False):
     """
     Construct an exponential kernel
@@ -147,6 +189,7 @@ def exponential(input_dim,variance=1., lengthscale=None, ARD=False):
     :type lengthscale: float
     :param ARD: Auto Relevance Determination (one lengthscale per dimension)
     :type ARD: Boolean
+
     """
     part = parts.exponential.Exponential(input_dim,variance, lengthscale, ARD)
     return kern(input_dim, [part])
@@ -163,6 +206,7 @@ def Matern32(input_dim,variance=1., lengthscale=None, ARD=False):
     :type lengthscale: float
     :param ARD: Auto Relevance Determination (one lengthscale per dimension)
     :type ARD: Boolean
+
     """
     part = parts.Matern32.Matern32(input_dim,variance, lengthscale, ARD)
     return kern(input_dim, [part])
@@ -179,6 +223,7 @@ def Matern52(input_dim, variance=1., lengthscale=None, ARD=False):
     :type lengthscale: float
     :param ARD: Auto Relevance Determination (one lengthscale per dimension)
     :type ARD: Boolean
+
     """
     part = parts.Matern52.Matern52(input_dim, variance, lengthscale, ARD)
     return kern(input_dim, [part])
@@ -187,10 +232,11 @@ def bias(input_dim, variance=1.):
     """
      Construct a bias kernel.
 
-     Arguments
+    :param input_dim: dimensionality of the kernel, obligatory
-     ---------
+    :type input_dim: int
-     input_dim (int), obligatory
+    :param variance: the variance of the kernel
-     variance (float)
+    :type variance: float
+
     """
     part = parts.bias.Bias(input_dim, variance)
     return kern(input_dim, [part])
@@ -198,10 +244,15 @@ def bias(input_dim, variance=1.):
 def finite_dimensional(input_dim, F, G, variances=1., weights=None):
     """
     Construct a finite dimensional kernel.
-    input_dim: int - the number of input dimensions
+
-    F: np.array of functions with shape (n,) - the n basis functions
+    :param input_dim: the number of input dimensions
-    G: np.array with shape (n,n) - the Gram matrix associated to F
+    :type input_dim: int
-    variances : np.ndarray with shape (n,)
+    :param F: np.array of functions with shape (n,) - the n basis functions
+    :type F: np.array
+    :param G: np.array with shape (n,n) - the Gram matrix associated to F
+    :type G: np.array
+    :param variances: np.ndarray with shape (n,)
+    :type: np.ndarray
     """
     part = parts.finite_dimensional.FiniteDimensional(input_dim, F, G, variances, weights)
     return kern(input_dim, [part])
@@ -214,6 +265,7 @@ def spline(input_dim, variance=1.):
     :type input_dim: int
     :param variance: the variance of the kernel
     :type variance: float
+
     """
     part = parts.spline.Spline(input_dim, variance)
     return kern(input_dim, [part])
@@ -226,43 +278,78 @@ def Brownian(input_dim, variance=1.):
     :type input_dim: int
     :param variance: the variance of the kernel
     :type variance: float
+
     """
     part = parts.Brownian.Brownian(input_dim, variance)
     return kern(input_dim, [part])
 
 try:
     import sympy as sp
-    from sympykern import spkern
-    from sympy.parsing.sympy_parser import parse_expr
     sympy_available = True
 except ImportError:
     sympy_available = False
 
 if sympy_available:
+    from parts.sympykern import spkern
+    from sympy.parsing.sympy_parser import parse_expr
+    from GPy.util.symbolic import sinc
+    
     def rbf_sympy(input_dim, ARD=False, variance=1., lengthscale=1.):
         """
         Radial Basis Function covariance.
         """
         X = [sp.var('x%i' % i) for i in range(input_dim)]
         Z = [sp.var('z%i' % i) for i in range(input_dim)]
-        rbf_variance = sp.var('rbf_variance',positive=True)
+        variance = sp.var('variance',positive=True)
         if ARD:
-            rbf_lengthscales = [sp.var('rbf_lengthscale_%i' % i, positive=True) for i in range(input_dim)]
+            lengthscales = [sp.var('lengthscale_%i' % i, positive=True) for i in range(input_dim)]
-            dist_string = ' + '.join(['(x%i-z%i)**2/rbf_lengthscale_%i**2' % (i, i, i) for i in range(input_dim)])
+            dist_string = ' + '.join(['(x%i-z%i)**2/lengthscale_%i**2' % (i, i, i) for i in range(input_dim)])
             dist = parse_expr(dist_string)
-            f =  rbf_variance*sp.exp(-dist/2.)
+            f =  variance*sp.exp(-dist/2.)
         else:
-            rbf_lengthscale = sp.var('rbf_lengthscale',positive=True)
+            lengthscale = sp.var('lengthscale',positive=True)
             dist_string = ' + '.join(['(x%i-z%i)**2' % (i, i) for i in range(input_dim)])
             dist = parse_expr(dist_string)
-            f =  rbf_variance*sp.exp(-dist/(2*rbf_lengthscale**2))
+            f =  variance*sp.exp(-dist/(2*lengthscale**2))
-        return kern(input_dim, [spkern(input_dim, f)])
+        return kern(input_dim, [spkern(input_dim, f, name='rbf_sympy')])
 
-    def sympykern(input_dim, k):
+    def sinc(input_dim, ARD=False, variance=1., lengthscale=1.):
         """
-        A kernel from a symbolic sympy representation
+        TODO: Not clear why this isn't working, suggests argument of sinc is not a number.
+        sinc covariance funciton
         """
-        return kern(input_dim, [spkern(input_dim, k)])
+        X = [sp.var('x%i' % i) for i in range(input_dim)]
+        Z = [sp.var('z%i' % i) for i in range(input_dim)]
+        variance = sp.var('variance',positive=True)
+        if ARD:
+            lengthscales = [sp.var('lengthscale_%i' % i, positive=True) for i in range(input_dim)]
+            dist_string = ' + '.join(['(x%i-z%i)**2/lengthscale_%i**2' % (i, i, i) for i in range(input_dim)])
+            dist = parse_expr(dist_string)
+            f =  variance*sinc(sp.pi*sp.sqrt(dist))
+        else:
+            lengthscale = sp.var('lengthscale',positive=True)
+            dist_string = ' + '.join(['(x%i-z%i)**2' % (i, i) for i in range(input_dim)])
+            dist = parse_expr(dist_string)
+            f =  variance*sinc(sp.pi*sp.sqrt(dist)/lengthscale)
+            
+        return kern(input_dim, [spkern(input_dim, f, name='sinc')])
+
+    def sympykern(input_dim, k,name=None):
+        """
+        A base kernel object, where all the hard work in done by sympy.
+
+        :param k: the covariance function
+        :type k: a positive definite sympy function of x1, z1, x2, z2...
+
+        To construct a new sympy kernel, you'll need to define:
+         - a kernel function using a sympy object. Ensure that the kernel is of the form k(x,z).
+         - that's it! we'll extract the variables from the function k.
+
+        Note:
+         - to handle multiple inputs, call them x1, z1, etc
+         - to handle multpile correlated outputs, you'll need to define each covariance function and 'cross' variance function. TODO
+        """
+        return kern(input_dim, [spkern(input_dim, k,name)])
 del sympy_available
 
 def periodic_exponential(input_dim=1, variance=1., lengthscale=None, period=2 * np.pi, n_freq=10, lower=0., upper=4 * np.pi):
@@ -279,6 +366,7 @@ def periodic_exponential(input_dim=1, variance=1., lengthscale=None, period=2 *
     :type period: float
     :param n_freq: the number of frequencies considered for the periodic subspace
     :type n_freq: int
+
     """
     part = parts.periodic_exponential.PeriodicExponential(input_dim, variance, lengthscale, period, n_freq, lower, upper)
     return kern(input_dim, [part])
@@ -297,6 +385,7 @@ def periodic_Matern32(input_dim, variance=1., lengthscale=None, period=2 * np.pi
      :type period: float
      :param n_freq: the number of frequencies considered for the periodic subspace
      :type n_freq: int
+
     """
     part = parts.periodic_Matern32.PeriodicMatern32(input_dim, variance, lengthscale, period, n_freq, lower, upper)
     return kern(input_dim, [part])
@@ -315,6 +404,7 @@ def periodic_Matern52(input_dim, variance=1., lengthscale=None, period=2 * np.pi
      :type period: float
      :param n_freq: the number of frequencies considered for the periodic subspace
      :type n_freq: int
+
     """
     part = parts.periodic_Matern52.PeriodicMatern52(input_dim, variance, lengthscale, period, n_freq, lower, upper)
     return kern(input_dim, [part])
@@ -328,6 +418,7 @@ def prod(k1,k2,tensor=False):
     :param tensor: The kernels are either multiply as functions defined on the same input space (default) or on the product of the input spaces
     :type tensor: Boolean
     :rtype: kernel object
+
     """
     part = parts.prod.Prod(k1, k2, tensor)
     return kern(part.input_dim, [part])
@@ -340,29 +431,32 @@ def symmetric(k):
     k_.parts = [symmetric.Symmetric(p) for p in k.parts]
     return k_
 
-def coregionalise(output_dim, rank=1, W=None, kappa=None):
+def coregionalize(output_dim,rank=1, W=None, kappa=None):
     """
-        Coregionalisation kernel. 
+    Coregionlization matrix B, of the form:
 
-    Used for computing covariance functions of the form
-    .. math::
-       k_2(x, y)=\mathbf{B} k(x, y)
-    where
     .. math::
        \mathbf{B} = \mathbf{W}\mathbf{W}^\top + kappa \mathbf{I}
 
-    :param output_dim: the number of output dimensions
+    An intrinsic/linear coregionalization kernel of the form:
+
+    .. math::
+       k_2(x, y)=\mathbf{B} k(x, y)
+
+    it is obtainded as the tensor product between a kernel k(x,y) and B.
+
+    :param output_dim: the number of outputs to corregionalize
     :type output_dim: int
-    :param rank: the rank of the coregionalisation matrix.
+    :param rank: number of columns of the W matrix (this parameter is ignored if parameter W is not None)
     :type rank: int
-    :param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalisation matrix B.
+    :param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalization matrix B
-    :type W: ndarray
+    :type W: numpy array of dimensionality (num_outpus, rank)
-    :param kappa: a diagonal term which allows the outputs to behave independently.
+    :param kappa: a vector which allows the outputs to behave independently
+    :type kappa: numpy array of dimensionality  (output_dim,)
     :rtype: kernel object
 
-    .. Note: see coregionalisation examples in GPy.examples.regression for some usage.
     """
-    p = parts.coregionalise.Coregionalise(output_dim,rank,W,kappa)
+    p = parts.coregionalize.Coregionalize(output_dim,rank,W,kappa)
     return kern(1,[p])
 
 
@@ -415,9 +509,58 @@ def independent_outputs(k):
 
 def hierarchical(k):
     """
-    TODO THis can't be right! Construct a kernel with independent outputs from an existing kernel
+    TODO This can't be right! Construct a kernel with independent outputs from an existing kernel
     """
     # for sl in k.input_slices:
     #     assert (sl.start is None) and (sl.stop is None), "cannot adjust input slices! (TODO)"
     _parts = [parts.hierarchical.Hierarchical(k.parts)]
     return kern(k.input_dim+len(k.parts),_parts)
+
+def build_lcm(input_dim, output_dim, kernel_list = [], rank=1,W=None,kappa=None):
+    """
+    Builds a kernel of a linear coregionalization model
+
+    :input_dim: Input dimensionality
+    :output_dim: Number of outputs
+    :kernel_list: List of coregionalized kernels, each element in the list will be multiplied by a different corregionalization matrix
+    :type kernel_list: list of GPy kernels
+    :param rank: number tuples of the corregionalization parameters 'coregion_W'
+    :type rank: integer
+
+    ..note the kernels dimensionality is overwritten to fit input_dim
+
+    """
+
+    for k in kernel_list:
+        if k.input_dim <> input_dim:
+            k.input_dim = input_dim
+            warnings.warn("kernel's input dimension overwritten to fit input_dim parameter.")
+
+    k_coreg = coregionalize(output_dim,rank,W,kappa)
+    kernel = kernel_list[0]**k_coreg.copy()
+
+    for k in kernel_list[1:]:
+        k_coreg = coregionalize(output_dim,rank,W,kappa)
+        kernel += k**k_coreg.copy()
+
+    return kernel
+
+def ODE_1(input_dim=1, varianceU=1.,  varianceY=1., lengthscaleU=None,  lengthscaleY=None):
+    """
+    kernel resultiong from a first order ODE with OU driving GP
+
+    :param input_dim: the number of input dimension, has to be equal to one
+    :type input_dim: int
+    :param varianceU: variance of the driving GP
+    :type varianceU: float
+    :param lengthscaleU: lengthscale of the driving GP
+    :type lengthscaleU: float
+    :param varianceY: 'variance' of the transfer function
+    :type varianceY: float
+    :param lengthscaleY: 'lengthscale' of the transfer function
+    :type lengthscaleY: float
+    :rtype: kernel object
+
+    """
+    part = parts.ODE_1.ODE_1(input_dim, varianceU, varianceY, lengthscaleU, lengthscaleY)
+    return kern(input_dim, [part])

GPy/kern/kern.py

@@ -1,6 +1,7 @@
 # Copyright (c) 2012, GPy authors (see AUTHORS.txt).
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
+import sys
 import numpy as np
 import pylab as pb
 from ..core.parameterized import Parameterized
@@ -12,7 +13,9 @@ from matplotlib.transforms import offset_copy
 class kern(Parameterized):
     def __init__(self, input_dim, parts=[], input_slices=None):
         """
-        This is the main kernel class for GPy. It handles multiple (additive) kernel functions, and keeps track of variaous things like which parameters live where.
+        This is the main kernel class for GPy. It handles multiple
+        (additive) kernel functions, and keeps track of various things
+        like which parameters live where.
 
         The technical code for kernels is divided into _parts_ (see
         e.g. rbf.py). This object contains a list of parts, which are
@@ -33,6 +36,11 @@ class kern(Parameterized):
 
         self.input_dim = input_dim
 
+        part_names = [k.name for k in self.parts]
+        self.name=''
+        for name in part_names:
+            self.name += name + '+'
+        self.name = self.name[:-1]
         # deal with input_slices
         if input_slices is None:
             self.input_slices = [slice(None) for p in self.parts]
@@ -71,13 +79,15 @@ class kern(Parameterized):
 
 
     def plot_ARD(self, fignum=None, ax=None, title='', legend=False):
-        """If an ARD kernel is present, it bar-plots the ARD parameters,
+        """If an ARD kernel is present, it bar-plots the ARD parameters.
+
         :param fignum: figure number of the plot
         :param ax: matplotlib axis to plot on
         :param title: 
             title of the plot, 
             pass '' to not print a title
             pass None for a generic title
+
         """
         if ax is None:
             fig = pb.figure(fignum)
@@ -168,8 +178,10 @@ class kern(Parameterized):
     def add(self, other, tensor=False):
         """
         Add another kernel to this one. Both kernels are defined on the same _space_
+
         :param other: the other kernel to be added
         :type other: GPy.kern
+
         """
         if tensor:
             D = self.input_dim + other.input_dim
@@ -211,11 +223,13 @@ class kern(Parameterized):
 
     def prod(self, other, tensor=False):
         """
-        multiply two kernels (either on the same space, or on the tensor product of the input space).
+        Multiply two kernels (either on the same space, or on the tensor product of the input space).
+
         :param other: the other kernel to be added
         :type other: GPy.kern
         :param tensor: whether or not to use the tensor space (default is false).
         :type tensor: bool 
+
         """
         K1 = self.copy()
         K2 = other.copy()
@@ -314,6 +328,7 @@ class kern(Parameterized):
         :type X: np.ndarray (num_samples x input_dim)
         :param X2: Observed data inputs (optional, defaults to X)
         :type X2: np.ndarray (num_inducing x input_dim)
+
         """
         assert X.shape[1] == self.input_dim
         target = np.zeros(self.num_params)
@@ -333,8 +348,7 @@ class kern(Parameterized):
         :type X: np.ndarray (num_samples x input_dim)
         :param X2: Observed data inputs (optional, defaults to X)
         :type X2: np.ndarray (num_inducing x input_dim)"""
-        if X2 is None:
+
-            X2 = X
         target = np.zeros_like(X)
         if X2 is None: 
             [p.dK_dX(dL_dK, X[:, i_s], None, target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
@@ -408,6 +422,7 @@ class kern(Parameterized):
         :param Z: np.ndarray of inducing inputs (num_inducing x input_dim)
         :param mu, S: np.ndarrays of means and variances (each num_samples x input_dim)
         :returns psi2: np.ndarray (num_samples,num_inducing,num_inducing)
+
         """
         target = np.zeros((mu.shape[0], Z.shape[0], Z.shape[0]))
         [p.psi2(Z[:, i_s], mu[:, i_s], S[:, i_s], target) for p, i_s in zip(self.parts, self.input_slices)]
@@ -563,7 +578,7 @@ class Kern_check_model(Model):
 
     def is_positive_definite(self):
         v = np.linalg.eig(self.kernel.K(self.X))[0]
-        if any(v<0):
+        if any(v<-10*sys.float_info.epsilon):
             return False
         else:
             return True
@@ -652,18 +667,102 @@ def kern_test(kern, X=None, X2=None, verbose=False):
     :type X: ndarray
     :param X2: X2 input values to test the covariance function.
     :type X2: ndarray
+
     """
+    pass_checks = True
     if X==None:
         X = np.random.randn(10, kern.input_dim)
     if X2==None:
         X2 = np.random.randn(20, kern.input_dim)
-    result = [Kern_check_model(kern, X=X).is_positive_definite(),
+    if verbose:
-              Kern_check_dK_dtheta(kern, X=X, X2=X2).checkgrad(verbose=verbose),
+        print("Checking covariance function is positive definite.")
-              Kern_check_dK_dtheta(kern, X=X, X2=None).checkgrad(verbose=verbose),
+    result = Kern_check_model(kern, X=X).is_positive_definite()
-             Kern_check_dKdiag_dtheta(kern, X=X).checkgrad(verbose=verbose),
+    if result and verbose:
-              Kern_check_dK_dX(kern, X=X, X2=X2).checkgrad(verbose=verbose),
+        print("Check passed.")
-              Kern_check_dKdiag_dX(kern, X=X).checkgrad(verbose=verbose)]
+    if not result:
-    # Need to check 
+        print("Positive definite check failed for " + kern.name + " covariance function.")
-    #Kern_check_dK_dX(kern, X, X2=None).checkgrad(verbose=verbose)]
+        pass_checks = False
-    # but currently I think these aren't implemented.
+        return False
-    return np.all(result)
+
+    if verbose:
+        print("Checking gradients of K(X, X) wrt theta.")
+    result = Kern_check_dK_dtheta(kern, X=X, X2=None).checkgrad(verbose=verbose)
+    if result and verbose:
+        print("Check passed.")
+    if not result:
+        print("Gradient of K(X, X) wrt theta failed for " + kern.name + " covariance function. Gradient values as follows:")
+        Kern_check_dK_dtheta(kern, X=X, X2=None).checkgrad(verbose=True)
+        pass_checks = False
+        return False
+
+    if verbose:
+        print("Checking gradients of K(X, X2) wrt theta.")
+    result = Kern_check_dK_dtheta(kern, X=X, X2=X2).checkgrad(verbose=verbose)
+    if result and verbose:
+        print("Check passed.")
+    if not result:
+        print("Gradient of K(X, X) wrt theta failed for " + kern.name + " covariance function. Gradient values as follows:")
+        Kern_check_dK_dtheta(kern, X=X, X2=X2).checkgrad(verbose=True)
+        pass_checks = False
+        return False
+
+    if verbose:
+        print("Checking gradients of Kdiag(X) wrt theta.")
+    result = Kern_check_dKdiag_dtheta(kern, X=X).checkgrad(verbose=verbose)
+    if result and verbose:
+        print("Check passed.")
+    if not result:
+        print("Gradient of Kdiag(X) wrt theta failed for " + kern.name + " covariance function. Gradient values as follows:")
+        Kern_check_dKdiag_dtheta(kern, X=X).checkgrad(verbose=True)
+        pass_checks = False
+        return False
+
+    if verbose:
+        print("Checking gradients of K(X, X) wrt X.")
+    try:
+        result = Kern_check_dK_dX(kern, X=X, X2=None).checkgrad(verbose=verbose)
+    except NotImplementedError:
+        result=True
+        if verbose:
+            print("dK_dX not implemented for " + kern.name)
+    if result and verbose:
+        print("Check passed.")
+    if not result:
+        print("Gradient of K(X, X) wrt X failed for " + kern.name + " covariance function. Gradient values as follows:")
+        Kern_check_dK_dX(kern, X=X, X2=None).checkgrad(verbose=True)
+        pass_checks = False
+        return False
+
+    if verbose:
+        print("Checking gradients of K(X, X2) wrt X.")
+    try:
+        result = Kern_check_dK_dX(kern, X=X, X2=X2).checkgrad(verbose=verbose)
+    except NotImplementedError:
+        result=True
+        if verbose:
+            print("dK_dX not implemented for " + kern.name)
+    if result and verbose:
+        print("Check passed.")
+    if not result:
+        print("Gradient of K(X, X) wrt X failed for " + kern.name + " covariance function. Gradient values as follows:")
+        Kern_check_dK_dX(kern, X=X, X2=X2).checkgrad(verbose=True)
+        pass_checks = False
+        return False
+
+    if verbose:
+        print("Checking gradients of Kdiag(X) wrt X.")
+    try:
+        result = Kern_check_dKdiag_dX(kern, X=X).checkgrad(verbose=verbose)
+    except NotImplementedError:
+        result=True
+        if verbose:
+            print("dK_dX not implemented for " + kern.name)
+    if result and verbose:
+        print("Check passed.")
+    if not result:
+        print("Gradient of Kdiag(X) wrt X failed for " + kern.name + " covariance function. Gradient values as follows:")
+        Kern_check_dKdiag_dX(kern, X=X).checkgrad(verbose=True)
+        pass_checks = False
+        return False
+
+    return pass_checks

GPy/kern/parts/Matern32.py

@@ -98,7 +98,11 @@ class Matern32(Kernpart):
 
     def dK_dX(self, dL_dK, X, X2, target):
         """derivative of the covariance matrix with respect to X."""
-        if X2 is None: X2 = X
+        if X2 is None:
+            dist = np.sqrt(np.sum(np.square((X[:, None, :] - X[None, :, :]) / self.lengthscale), -1))[:, :, None]
+            ddist_dX = 2*(X[:, None, :] - X[None, :, :]) / self.lengthscale ** 2 / np.where(dist != 0., dist, np.inf)
+
+        else:
             dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1))[:, :, None]
             ddist_dX = (X[:, None, :] - X2[None, :, :]) / self.lengthscale ** 2 / np.where(dist != 0., dist, np.inf)
         dK_dX = -np.transpose(3 * self.variance * dist * np.exp(-np.sqrt(3) * dist) * ddist_dX, (1, 0, 2))

GPy/kern/parts/Matern52.py

@@ -98,7 +98,10 @@ class Matern52(Kernpart):
 
     def dK_dX(self,dL_dK,X,X2,target):
         """derivative of the covariance matrix with respect to X."""
-        if X2 is None: X2 = X
+        if X2 is None:
+            dist = np.sqrt(np.sum(np.square((X[:,None,:]-X[None,:,:])/self.lengthscale),-1))[:,:,None]
+            ddist_dX = 2*(X[:,None,:]-X[None,:,:])/self.lengthscale**2/np.where(dist!=0.,dist,np.inf)
+        else:
             dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))[:,:,None]
             ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscale**2/np.where(dist!=0.,dist,np.inf)
         dK_dX = -  np.transpose(self.variance*5./3*dist*(1+np.sqrt(5)*dist)*np.exp(-np.sqrt(5)*dist)*ddist_dX,(1,0,2))

GPy/kern/parts/ODE_1.py

@@ -0,0 +1,161 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+from kernpart import Kernpart
+import numpy as np
+
+class ODE_1(Kernpart):
+    """
+    kernel resultiong from a first order ODE with OU driving GP
+
+    :param input_dim: the number of input dimension, has to be equal to one
+    :type input_dim: int
+    :param varianceU: variance of the driving GP
+    :type varianceU: float
+    :param lengthscaleU: lengthscale of the driving GP  (sqrt(3)/lengthscaleU)
+    :type lengthscaleU: float
+    :param varianceY: 'variance' of the transfer function
+    :type varianceY: float
+    :param lengthscaleY: 'lengthscale' of the transfer function (1/lengthscaleY)
+    :type lengthscaleY: float
+    :rtype: kernel object
+
+    """
+    def __init__(self, input_dim=1, varianceU=1., varianceY=1., lengthscaleU=None, lengthscaleY=None):
+        assert input_dim==1, "Only defined for input_dim = 1"
+        self.input_dim = input_dim
+        self.num_params = 4
+        self.name = 'ODE_1'
+        if lengthscaleU is not None:
+            lengthscaleU = np.asarray(lengthscaleU)
+            assert lengthscaleU.size == 1, "lengthscaleU should be one dimensional"
+        else:
+            lengthscaleU = np.ones(1)
+        if lengthscaleY is not None:
+            lengthscaleY = np.asarray(lengthscaleY)
+            assert lengthscaleY.size == 1, "lengthscaleY should be one dimensional"
+        else:
+            lengthscaleY = np.ones(1)
+            #lengthscaleY = 0.5
+        self._set_params(np.hstack((varianceU, varianceY, lengthscaleU,lengthscaleY)))
+
+    def _get_params(self):
+        """return the value of the parameters."""
+        return np.hstack((self.varianceU,self.varianceY, self.lengthscaleU,self.lengthscaleY))
+
+    def _set_params(self, x):
+        """set the value of the parameters."""
+        assert x.size == self.num_params
+        self.varianceU = x[0]
+        self.varianceY = x[1]
+        self.lengthscaleU = x[2]
+        self.lengthscaleY = x[3]
+
+    def _get_param_names(self):
+        """return parameter names."""
+        return ['varianceU','varianceY', 'lengthscaleU', 'lengthscaleY']
+
+
+    def K(self, X, X2, target):
+        """Compute the covariance matrix between X and X2."""
+        if X2 is None: X2 = X
+       # i1 = X[:,1]
+       # i2 = X2[:,1]
+       # X = X[:,0].reshape(-1,1)
+       # X2 = X2[:,0].reshape(-1,1)
+        dist = np.abs(X - X2.T)
+        
+        ly=1/self.lengthscaleY
+        lu=np.sqrt(3)/self.lengthscaleU
+        #ly=self.lengthscaleY
+        #lu=self.lengthscaleU
+
+        k1 = np.exp(-ly*dist)*(2*lu+ly)/(lu+ly)**2
+        k2 = (np.exp(-lu*dist)*(ly-2*lu+lu*ly*dist-lu**2*dist) + np.exp(-ly*dist)*(2*lu-ly) ) / (ly-lu)**2 
+        k3 = np.exp(-lu*dist) * ( (1+lu*dist)/(lu+ly) + (lu)/(lu+ly)**2 )
+
+        np.add(self.varianceU*self.varianceY*(k1+k2+k3), target, target)
+
+    def Kdiag(self, X, target):
+        """Compute the diagonal of the covariance matrix associated to X."""
+        ly=1/self.lengthscaleY
+        lu=np.sqrt(3)/self.lengthscaleU
+        #ly=self.lengthscaleY
+        #lu=self.lengthscaleU
+        
+        k1 = (2*lu+ly)/(lu+ly)**2
+        k2 = (ly-2*lu + 2*lu-ly ) / (ly-lu)**2 
+        k3 = 1/(lu+ly) + (lu)/(lu+ly)**2 
+
+        np.add(self.varianceU*self.varianceY*(k1+k2+k3), target, target)
+
+    def dK_dtheta(self, dL_dK, X, X2, target):
+        """derivative of the covariance matrix with respect to the parameters."""
+        if X2 is None: X2 = X
+        dist = np.abs(X - X2.T)
+
+        ly=1/self.lengthscaleY
+        lu=np.sqrt(3)/self.lengthscaleU
+        #ly=self.lengthscaleY
+        #lu=self.lengthscaleU
+
+        dk1theta1 = np.exp(-ly*dist)*2*(-lu)/(lu+ly)**3
+        #c=np.sqrt(3)
+        #t1=c/lu
+        #t2=1/ly
+        #dk1theta1=np.exp(-dist*ly)*t2*( (2*c*t2+2*t1)/(c*t2+t1)**2 -2*(2*c*t2*t1+t1**2)/(c*t2+t1)**3   )
+        
+        dk2theta1 = 1*( 
+            np.exp(-lu*dist)*dist*(-ly+2*lu-lu*ly*dist+dist*lu**2)*(ly-lu)**(-2) + np.exp(-lu*dist)*(-2+ly*dist-2*dist*lu)*(ly-lu)**(-2) 
+            +np.exp(-dist*lu)*(ly-2*lu+ly*lu*dist-dist*lu**2)*2*(ly-lu)**(-3) 
+            +np.exp(-dist*ly)*2*(ly-lu)**(-2)
+            +np.exp(-dist*ly)*2*(2*lu-ly)*(ly-lu)**(-3)
+            )
+      
+        dk3theta1 = np.exp(-dist*lu)*(lu+ly)**(-2)*((2*lu+ly+dist*lu**2+lu*ly*dist)*(-dist-2/(lu+ly))+2+2*lu*dist+ly*dist)
+
+        dktheta1 = self.varianceU*self.varianceY*(dk1theta1+dk2theta1+dk3theta1)
+
+
+
+
+        dk1theta2 = np.exp(-ly*dist) * ((lu+ly)**(-2)) * (  (-dist)*(2*lu+ly)  +  1  +  (-2)*(2*lu+ly)/(lu+ly)  )
+
+        dk2theta2 = 1*(
+            np.exp(-dist*lu)*(ly-lu)**(-2) * ( 1+lu*dist+(-2)*(ly-2*lu+lu*ly*dist-dist*lu**2)*(ly-lu)**(-1) )
+            +np.exp(-dist*ly)*(ly-lu)**(-2) * ( (-dist)*(2*lu-ly) -1+(2*lu-ly)*(-2)*(ly-lu)**(-1) )
+            )
+
+        dk3theta2 = np.exp(-dist*lu) * (-3*lu-ly-dist*lu**2-lu*ly*dist)/(lu+ly)**3
+
+        dktheta2 = self.varianceU*self.varianceY*(dk1theta2 + dk2theta2 +dk3theta2)
+
+
+
+        k1 = np.exp(-ly*dist)*(2*lu+ly)/(lu+ly)**2
+        k2 = (np.exp(-lu*dist)*(ly-2*lu+lu*ly*dist-lu**2*dist) + np.exp(-ly*dist)*(2*lu-ly) ) / (ly-lu)**2 
+        k3 = np.exp(-lu*dist) * ( (1+lu*dist)/(lu+ly) + (lu)/(lu+ly)**2 )
+        dkdvar = k1+k2+k3
+
+        target[0] += np.sum(self.varianceY*dkdvar * dL_dK)
+        target[1] += np.sum(self.varianceU*dkdvar * dL_dK)
+        target[2] += np.sum(dktheta1*(-np.sqrt(3)*self.lengthscaleU**(-2)) * dL_dK)
+        target[3] += np.sum(dktheta2*(-self.lengthscaleY**(-2)) * dL_dK)
+
+
+    # def dKdiag_dtheta(self, dL_dKdiag, X, target):
+    #     """derivative of the diagonal of the covariance matrix with respect to the parameters."""
+    #     # NB: derivative of diagonal elements wrt lengthscale is 0
+    #     target[0] += np.sum(dL_dKdiag)
+
+    # def dK_dX(self, dL_dK, X, X2, target):
+    #     """derivative of the covariance matrix with respect to X."""
+    #     if X2 is None: X2 = X
+    #     dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1))[:, :, None]
+    #     ddist_dX = (X[:, None, :] - X2[None, :, :]) / self.lengthscale ** 2 / np.where(dist != 0., dist, np.inf)
+    #     dK_dX = -np.transpose(self.variance * np.exp(-dist) * ddist_dX, (1, 0, 2))
+    #     target += np.sum(dK_dX * dL_dK.T[:, :, None], 0)
+
+    # def dKdiag_dX(self, dL_dKdiag, X, target):
+    #     pass

GPy/kern/parts/__init__.py

@@ -1,15 +1,19 @@
 import bias
 import Brownian
-import coregionalise
+import coregionalize
 import exponential
+import eq_ode1
 import finite_dimensional
 import fixed
 import gibbs
+import hetero
+import hierarchical
 import independent_outputs
 import linear
 import Matern32
 import Matern52
 import mlp
+import ODE_1
 import periodic_exponential
 import periodic_Matern32
 import periodic_Matern52
@@ -19,8 +23,7 @@ import prod
 import rational_quadratic
 import rbfcos
 import rbf
+import rbf_inv
 import spline
 import symmetric
 import white
-import hierarchical
-import rbf_inv

GPy/kern/parts/coregionalize.py

@@ -7,33 +7,40 @@ from GPy.util.linalg import mdot, pdinv
 import pdb
 from scipy import weave
 
-class Coregionalise(Kernpart):
+class Coregionalize(Kernpart):
     """
-    Coregionalisation kernel. 
+    Covariance function for intrinsic/linear coregionalization models
 
-    Used for computing covariance functions of the form
+    This covariance has the form:
     .. math::
-       k_2(x, y)=B k(x, y)
+       \mathbf{B} = \mathbf{W}\mathbf{W}^\top + \text{diag}(kappa)
-    where
-    .. math::
-       B = WW^\top + diag(kappa)
 
-    :param output_dim: the number of output dimensions
+    An intrinsic/linear coregionalization covariance function of the form:
+    .. math::
+
+       k_2(x, y)=\mathbf{B} k(x, y)
+
+    it is obtained as the tensor product between a covariance function
+    k(x,y) and B.
+
+    :param output_dim: number of outputs to coregionalize
     :type output_dim: int
-    :param rank: the rank of the coregionalisation matrix.
+    :param rank: number of columns of the W matrix (this parameter is ignored if parameter W is not None)
     :type rank: int
-    :param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalisation matrix B.
+    :param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalization matrix B
-    :type W: ndarray
+    :type W: numpy array of dimensionality (num_outpus, W_columns)
-    :param kappa: a diagonal term which allows the outputs to behave independently.
+    :param kappa: a vector which allows the outputs to behave independently
-    :rtype: kernel object
+    :type kappa: numpy array of dimensionality  (output_dim,)
 
-    .. Note: see coregionalisation examples in GPy.examples.regression for some usage.
+    .. note: see coregionalization examples in GPy.examples.regression for some usage.
     """
-    def __init__(self,output_dim,rank=1, W=None, kappa=None):
+    def __init__(self, output_dim, rank=1, W=None, kappa=None):
         self.input_dim = 1
         self.name = 'coregion'
         self.output_dim = output_dim
         self.rank = rank
+        if self.rank>output_dim-1:
+            print("Warning: Unusual choice of rank, it should normally be less than the output_dim.")
         if W is None:
             self.W = 0.5*np.random.randn(self.output_dim,self.rank)/np.sqrt(self.rank)
         else:
@@ -154,7 +161,5 @@ class Coregionalise(Kernpart):
         target += np.hstack([dW.flatten(),dkappa])
 
     def dK_dX(self,dL_dK,X,X2,target):
+        #NOTE In this case, pass is equivalent to returning zero.
         pass
-
-
-

GPy/kern/parts/eq_ode1.py

@@ -0,0 +1,556 @@
+# Copyright (c) 2013, GPy Authors, see AUTHORS.txt
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+from kernpart import Kernpart
+import numpy as np
+from GPy.util.linalg import mdot, pdinv
+from GPy.util.ln_diff_erfs import ln_diff_erfs
+import pdb
+from scipy import weave
+
+class Eq_ode1(Kernpart):
+    """
+    Covariance function for first order differential equation driven by an exponentiated quadratic covariance.
+
+    This outputs of this kernel have the form
+    .. math::
+       \frac{\text{d}y_j}{\text{d}t} = \sum_{i=1}^R w_{j,i} f_i(t-\delta_j) +\sqrt{\kappa_j}g_j(t) - d_jy_j(t)
+
+    where :math:`R` is the rank of the system, :math:`w_{j,i}` is the sensitivity of the :math:`j`th output to the :math:`i`th latent function, :math:`d_j` is the decay rate of the :math:`j`th output and :math:`f_i(t)` and :math:`g_i(t)` are independent latent Gaussian processes goverened by an exponentiated quadratic covariance.
+    
+    :param output_dim: number of outputs driven by latent function.
+    :type output_dim: int
+    :param W: sensitivities of each output to the latent driving function. 
+    :type W: ndarray (output_dim x rank).
+    :param rank: If rank is greater than 1 then there are assumed to be a total of rank latent forces independently driving the system, each with identical covariance.
+    :type rank: int
+    :param decay: decay rates for the first order system. 
+    :type decay: array of length output_dim.
+    :param delay: delay between latent force and output response.
+    :type delay: array of length output_dim.
+    :param kappa: diagonal term that allows each latent output to have an independent component to the response.
+    :type kappa: array of length output_dim.
+    
+    .. Note: see first order differential equation examples in GPy.examples.regression for some usage.
+    """
+    def __init__(self,output_dim, W=None, rank=1, kappa=None, lengthscale=1.0,  decay=None, delay=None):
+        self.rank = rank
+        self.input_dim = 1
+        self.name = 'eq_ode1'
+        self.output_dim = output_dim
+        self.lengthscale = lengthscale
+        self.num_params = self.output_dim*self.rank + 1 + (self.output_dim - 1)
+        if kappa is not None:
+            self.num_params+=self.output_dim
+        if delay is not None:
+            assert delay.shape==(self.output_dim-1,)
+            self.num_params+=self.output_dim-1
+        self.rank = rank
+        if W is None:
+            self.W = 0.5*np.random.randn(self.output_dim,self.rank)/np.sqrt(self.rank)
+        else:
+            assert W.shape==(self.output_dim,self.rank)
+            self.W = W
+        if decay is None:
+            self.decay = np.ones(self.output_dim-1)
+        if kappa is not None:
+            assert kappa.shape==(self.output_dim,)
+        self.kappa = kappa
+
+        self.delay = delay
+        self.is_normalized = True
+        self.is_stationary = False
+        self.gaussian_initial = False
+        self._set_params(self._get_params())
+        
+    def _get_params(self):
+        param_list = [self.W.flatten()]
+        if self.kappa is not None:
+            param_list.append(self.kappa)
+        param_list.append(self.decay)
+        if self.delay is not None:
+            param_list.append(self.delay)
+        param_list.append(self.lengthscale)
+        return np.hstack(param_list)
+
+    def _set_params(self,x):
+        assert x.size == self.num_params
+        end = self.output_dim*self.rank
+        self.W = x[:end].reshape(self.output_dim,self.rank)
+        start = end
+        self.B = np.dot(self.W,self.W.T)
+        if self.kappa is not None:
+            end+=self.output_dim
+            self.kappa = x[start:end]
+            self.B += np.diag(self.kappa)
+            start=end
+        end+=self.output_dim-1
+        self.decay = x[start:end]
+        start=end
+        if self.delay is not None:
+            end+=self.output_dim-1
+            self.delay = x[start:end]
+            start=end
+        end+=1
+        self.lengthscale = x[start]
+        self.sigma = np.sqrt(2)*self.lengthscale
+
+
+    def _get_param_names(self):
+        param_names = sum([['W%i_%i'%(i,j) for j in range(self.rank)] for i in range(self.output_dim)],[])
+        if self.kappa is not None:
+            param_names += ['kappa_%i'%i for i in range(self.output_dim)]
+        param_names += ['decay_%i'%i for i in range(1,self.output_dim)]
+        if self.delay is not None:
+            param_names += ['delay_%i'%i for i in 1+range(1,self.output_dim)]
+        param_names+= ['lengthscale'] 
+        return param_names
+
+    def K(self,X,X2,target):
+        
+        if X.shape[1] > 2:
+            raise ValueError('Input matrix for ode1 covariance should have at most two columns, one containing times, the other output indices')
+
+        self._K_computations(X, X2)
+        target += self._scale*self._K_dvar
+
+        if self.gaussian_initial:
+            # Add covariance associated with initial condition.
+            t1_mat = self._t[self._rorder, None]
+            t2_mat = self._t2[None, self._rorder2]
+            target+=self.initial_variance * np.exp(- self.decay * (t1_mat + t2_mat))
+
+    def Kdiag(self,index,target):
+        #target += np.diag(self.B)[np.asarray(index,dtype=np.int).flatten()]
+        pass
+    
+    def dK_dtheta(self,dL_dK,X,X2,target):
+        
+        # First extract times and indices.
+        self._extract_t_indices(X, X2, dL_dK=dL_dK)
+        self._dK_ode_dtheta(target)
+        
+
+    def _dK_ode_dtheta(self, target):
+        """Do all the computations for the ode parts of the covariance function."""
+        t_ode = self._t[self._index>0]
+        dL_dK_ode = self._dL_dK[self._index>0, :]
+        index_ode = self._index[self._index>0]-1
+        if self._t2 is None:
+            if t_ode.size==0:
+                return        
+            t2_ode = t_ode
+            dL_dK_ode = dL_dK_ode[:, self._index>0]
+            index2_ode = index_ode
+        else:
+            t2_ode = self._t2[self._index2>0]
+            dL_dK_ode = dL_dK_ode[:, self._index2>0]
+            if t_ode.size==0 or t2_ode.size==0:
+                return
+            index2_ode = self._index2[self._index2>0]-1
+
+        h1 = self._compute_H(t_ode, index_ode, t2_ode, index2_ode, stationary=self.is_stationary, update_derivatives=True)
+        #self._dK_ddelay = self._dh_ddelay
+        self._dK_dsigma = self._dh_dsigma
+
+        if self._t2 is None:
+            h2 = h1
+        else:
+            h2 = self._compute_H(t2_ode, index2_ode, t_ode, index_ode, stationary=self.is_stationary, update_derivatives=True)
+
+        #self._dK_ddelay += self._dh_ddelay.T
+        self._dK_dsigma += self._dh_dsigma.T
+        # C1 = self.sensitivity
+        # C2 = self.sensitivity
+
+        # K = 0.5 * (h1 + h2.T)
+        # var2 = C1*C2
+        # if self.is_normalized:
+        #     dk_dD1 = (sum(sum(dL_dK.*dh1_dD1)) + sum(sum(dL_dK.*dh2_dD1.T)))*0.5*var2
+        #     dk_dD2 = (sum(sum(dL_dK.*dh1_dD2)) + sum(sum(dL_dK.*dh2_dD2.T)))*0.5*var2
+        #     dk_dsigma = 0.5 * var2 * sum(sum(dL_dK.*dK_dsigma))
+        #     dk_dC1 = C2 * sum(sum(dL_dK.*K))
+        #     dk_dC2 = C1 * sum(sum(dL_dK.*K))
+        # else:
+        #     K = np.sqrt(np.pi) * K
+        #     dk_dD1 = (sum(sum(dL_dK.*dh1_dD1)) + * sum(sum(dL_dK.*K))
+        #     dk_dC2 = self.sigma * C1 * sum(sum(dL_dK.*K))
+
+
+        # dk_dSim1Variance = dk_dC1
+        # Last element is the length scale.
+        (dL_dK_ode[:, :, None]*self._dh_ddelay[:, None, :]).sum(2)
+
+        target[-1] += (dL_dK_ode*self._dK_dsigma/np.sqrt(2)).sum()
+
+
+        # # only pass the gradient with respect to the inverse width to one
+        # # of the gradient vectors ... otherwise it is counted twice.
+        # g1 = real([dk_dD1 dk_dinvWidth dk_dSim1Variance])
+        # g2 = real([dk_dD2 0 dk_dSim2Variance])
+        # return g1, g2"""
+
+    def dKdiag_dtheta(self,dL_dKdiag,index,target):
+        pass
+
+    def dK_dX(self,dL_dK,X,X2,target):
+        pass
+
+    def _extract_t_indices(self, X, X2=None, dL_dK=None):
+        """Extract times and output indices from the input matrix X. Times are ordered according to their index for convenience of computation, this ordering is stored in self._order and self.order2. These orderings are then mapped back to the original ordering (in X) using self._rorder and self._rorder2. """
+
+        # TODO: some fast checking here to see if this needs recomputing?
+        self._t = X[:, 0]
+        if not X.shape[1] == 2:
+            raise ValueError('Input matrix for ode1 covariance should have two columns, one containing times, the other output indices')
+        self._index = np.asarray(X[:, 1],dtype=np.int)
+        # Sort indices so that outputs are in blocks for computational
+        # convenience.
+        self._order = self._index.argsort()
+        self._index = self._index[self._order]
+        self._t = self._t[self._order]
+        self._rorder = self._order.argsort() # rorder is for reversing the order
+        
+        if X2 is None:
+            self._t2 = None
+            self._index2 = None
+            self._order2 = self._order
+            self._rorder2 = self._rorder
+        else:
+            if not X2.shape[1] == 2:
+                raise ValueError('Input matrix for ode1 covariance should have two columns, one containing times, the other output indices')
+            self._t2 = X2[:, 0]
+            self._index2 = np.asarray(X2[:, 1],dtype=np.int)
+            self._order2 = self._index2.argsort()
+            self._index2 = self._index2[self._order2]
+            self._t2 = self._t2[self._order2]
+            self._rorder2 = self._order2.argsort() # rorder2 is for reversing order
+
+        if dL_dK is not None:
+            self._dL_dK = dL_dK[self._order, :]
+            self._dL_dK = self._dL_dK[:, self._order2]
+            
+    def _K_computations(self, X, X2):
+        """Perform main body of computations for the ode1 covariance function."""
+        # First extract times and indices.
+        self._extract_t_indices(X, X2)
+
+        self._K_compute_eq()
+        self._K_compute_ode_eq()
+        if X2 is None:
+            self._K_eq_ode = self._K_ode_eq.T
+        else:
+            self._K_compute_ode_eq(transpose=True)
+        self._K_compute_ode()
+
+        if X2 is None:
+            self._K_dvar = np.zeros((self._t.shape[0], self._t.shape[0]))
+        else:
+            self._K_dvar = np.zeros((self._t.shape[0], self._t2.shape[0]))
+
+        # Reorder values of blocks for placing back into _K_dvar.
+        self._K_dvar = np.vstack((np.hstack((self._K_eq, self._K_eq_ode)),
+                                                   np.hstack((self._K_ode_eq, self._K_ode))))
+        self._K_dvar = self._K_dvar[self._rorder, :]
+        self._K_dvar = self._K_dvar[:, self._rorder2]
+        
+        
+        if X2 is None:
+            # Matrix giving scales of each output
+            self._scale = np.zeros((self._t.size, self._t.size))
+            code="""
+            for(int i=0;i<N; i++){
+              scale_mat[i+i*N] = B[index[i]+output_dim*(index[i])];
+              for(int j=0; j<i; j++){
+                  scale_mat[j+i*N] = B[index[i]+output_dim*index[j]];
+                  scale_mat[i+j*N] = scale_mat[j+i*N];
+                }
+              }
+            """
+            scale_mat, B, index = self._scale, self.B, self._index
+            N, output_dim = self._t.size, self.output_dim
+            weave.inline(code,['index',
+                               'scale_mat', 'B',
+                               'N', 'output_dim'])
+        else:
+            self._scale = np.zeros((self._t.size, self._t2.size))
+            code = """
+            for(int i=0; i<N; i++){
+              for(int j=0; j<N2; j++){
+                scale_mat[i+j*N] = B[index[i]+output_dim*index2[j]];
+              }
+            }
+            """
+            scale_mat, B, index, index2 = self._scale, self.B, self._index, self._index2
+            N, N2, output_dim = self._t.size, self._t2.size, self.output_dim
+            weave.inline(code, ['index', 'index2',
+                                'scale_mat', 'B',
+                                'N', 'N2', 'output_dim'])
+
+
+
+    def _K_compute_eq(self):
+        """Compute covariance for latent covariance."""
+        t_eq = self._t[self._index==0]
+        if self._t2 is None:
+            if t_eq.size==0:
+                self._K_eq = np.zeros((0, 0))
+                return
+            self._dist2 = np.square(t_eq[:, None] - t_eq[None, :])
+        else:
+            t2_eq = self._t2[self._index2==0]
+            if t_eq.size==0 or t2_eq.size==0:
+                self._K_eq = np.zeros((t_eq.size, t2_eq.size))
+                return
+            self._dist2 = np.square(t_eq[:, None] - t2_eq[None, :])
+        
+        self._K_eq = np.exp(-self._dist2/(2*self.lengthscale*self.lengthscale))
+        if self.is_normalized:
+            self._K_eq/=(np.sqrt(2*np.pi)*self.lengthscale)
+
+    def _K_compute_ode_eq(self, transpose=False):
+        """Compute the cross covariances between latent exponentiated quadratic and observed ordinary differential equations.
+
+        :param transpose: if set to false the exponentiated quadratic is on the rows of the matrix and is computed according to self._t, if set to true it is on the columns and is computed according to self._t2 (default=False).
+        :type transpose: bool"""
+
+        if self._t2 is not None:
+            if transpose:
+                t_eq = self._t[self._index==0]
+                t_ode = self._t2[self._index2>0]
+                index_ode = self._index2[self._index2>0]-1
+            else:
+                t_eq = self._t2[self._index2==0]
+                t_ode = self._t[self._index>0]
+                index_ode = self._index[self._index>0]-1
+        else:
+            t_eq = self._t[self._index==0]
+            t_ode = self._t[self._index>0]
+            index_ode = self._index[self._index>0]-1
+
+        if t_ode.size==0 or t_eq.size==0:
+            if transpose:
+                self._K_eq_ode = np.zeros((t_eq.shape[0], t_ode.shape[0]))
+            else:
+                self._K_ode_eq = np.zeros((t_ode.shape[0], t_eq.shape[0]))
+            return
+
+        t_ode_mat = t_ode[:, None]
+        t_eq_mat = t_eq[None, :]
+        if self.delay is not None:
+            t_ode_mat -= self.delay[index_ode, None]
+        diff_t = (t_ode_mat - t_eq_mat)
+
+        inv_sigma_diff_t = 1./self.sigma*diff_t
+        decay_vals = self.decay[index_ode][:, None]
+        half_sigma_d_i = 0.5*self.sigma*decay_vals
+
+        if self.is_stationary:
+            ln_part, signs = ln_diff_erfs(inf, half_sigma_d_i - inv_sigma_diff_t, return_sign=True)
+        else:
+            ln_part, signs = ln_diff_erfs(half_sigma_d_i + t_eq_mat/self.sigma, half_sigma_d_i - inv_sigma_diff_t, return_sign=True)
+        sK = signs*np.exp(half_sigma_d_i*half_sigma_d_i - decay_vals*diff_t + ln_part)
+
+        sK *= 0.5
+
+        if not self.is_normalized:
+            sK *= np.sqrt(np.pi)*self.sigma
+
+
+        if transpose:
+            self._K_eq_ode = sK.T
+        else:
+            self._K_ode_eq = sK
+        
+    def _K_compute_ode(self):
+        # Compute covariances between outputs of the ODE models.
+
+        t_ode = self._t[self._index>0]
+        index_ode = self._index[self._index>0]-1
+        if self._t2 is None:
+            if t_ode.size==0:
+                self._K_ode = np.zeros((0, 0))
+                return        
+            t2_ode = t_ode
+            index2_ode = index_ode
+        else:
+            t2_ode = self._t2[self._index2>0]
+            if t_ode.size==0 or t2_ode.size==0:
+                self._K_ode = np.zeros((t_ode.size, t2_ode.size))
+                return
+            index2_ode = self._index2[self._index2>0]-1
+        
+        # When index is identical
+        h = self._compute_H(t_ode, index_ode, t2_ode, index2_ode, stationary=self.is_stationary)
+
+        if self._t2 is None:
+            self._K_ode = 0.5 * (h + h.T)
+        else:
+            h2 = self._compute_H(t2_ode, index2_ode, t_ode, index_ode, stationary=self.is_stationary)                
+            self._K_ode = 0.5 * (h + h2.T)
+
+        if not self.is_normalized:
+            self._K_ode *= np.sqrt(np.pi)*self.sigma
+    def _compute_diag_H(self, t, index, update_derivatives=False, stationary=False):
+        """Helper function for computing H for the diagonal only.
+        :param t: time input.
+        :type t: array
+        :param index: first output indices
+        :type index: array of int.
+        :param index: second output indices
+        :type index: array of int.
+        :param update_derivatives: whether or not to update the derivative portions (default False).
+        :type update_derivatives: bool
+        :param stationary: whether to compute the stationary version of the covariance (default False).
+        :type stationary: bool"""
+
+        """if delta_i~=delta_j:
+            [h, dh_dD_i, dh_dD_j, dh_dsigma] = np.diag(simComputeH(t, index, t, index, update_derivatives=True, stationary=self.is_stationary))
+        else:
+            Decay = self.decay[index]
+            if self.delay is not None:
+                t = t - self.delay[index]
+            
+            t_squared = t*t
+            half_sigma_decay = 0.5*self.sigma*Decay
+            [ln_part_1, sign1] = ln_diff_erfs(half_sigma_decay + t/self.sigma,
+                                              half_sigma_decay)
+    
+            [ln_part_2, sign2] = ln_diff_erfs(half_sigma_decay,
+                                              half_sigma_decay - t/self.sigma)
+            
+            h = (sign1*np.exp(half_sigma_decay*half_sigma_decay
+                             + ln_part_1
+                             - log(Decay + D_j)) 
+                 - sign2*np.exp(half_sigma_decay*half_sigma_decay
+                                - (Decay + D_j)*t
+                                + ln_part_2 
+                                - log(Decay + D_j)))
+    
+            sigma2 = self.sigma*self.sigma
+
+        if update_derivatives:
+        
+            dh_dD_i = ((0.5*Decay*sigma2*(Decay + D_j)-1)*h 
+                       + t*sign2*np.exp(
+                half_sigma_decay*half_sigma_decay-(Decay+D_j)*t + ln_part_2
+                )
+                       + self.sigma/np.sqrt(np.pi)*
+                       (-1 + np.exp(-t_squared/sigma2-Decay*t)
+                        + np.exp(-t_squared/sigma2-D_j*t)
+                        - np.exp(-(Decay + D_j)*t)))
+        
+            dh_dD_i = (dh_dD_i/(Decay+D_j)).real
+        
+        
+        
+            dh_dD_j = (t*sign2*np.exp(
+                half_sigma_decay*half_sigma_decay-(Decay + D_j)*t+ln_part_2
+                )
+                       -h)
+            dh_dD_j = (dh_dD_j/(Decay + D_j)).real
+
+            dh_dsigma = 0.5*Decay*Decay*self.sigma*h \
+                        + 2/(np.sqrt(np.pi)*(Decay+D_j))\
+                        *((-Decay/2) \
+                          + (-t/sigma2+Decay/2)*np.exp(-t_squared/sigma2 - Decay*t) \
+                          - (-t/sigma2-Decay/2)*np.exp(-t_squared/sigma2 - D_j*t) \
+                          - Decay/2*np.exp(-(Decay+D_j)*t))"""
+        pass
+    
+    def _compute_H(self, t, index, t2, index2, update_derivatives=False, stationary=False):
+        """Helper function for computing part of the ode1 covariance function.
+
+        :param t: first time input.
+        :type t: array
+        :param index: Indices of first output.
+        :type index: array of int
+        :param t2: second time input.
+        :type t2: array
+        :param index2: Indices of second output.
+        :type index2: array of int
+        :param update_derivatives: whether to update derivatives (default is False)
+        :return h : result of this subcomponent of the kernel for the given values.
+        :rtype: ndarray
+"""
+
+        if stationary:
+            raise NotImplementedError, "Error, stationary version of this covariance not yet implemented."
+        # Vector of decays and delays associated with each output.
+        Decay = self.decay[index]
+        Decay2 = self.decay[index2]
+        t_mat = t[:, None]
+        t2_mat = t2[None, :]
+        if self.delay is not None:
+            Delay = self.delay[index]
+            Delay2 = self.delay[index2]
+            t_mat-=Delay[:, None]
+            t2_mat-=Delay2[None, :]
+
+        diff_t = (t_mat - t2_mat)
+        inv_sigma_diff_t = 1./self.sigma*diff_t
+        half_sigma_decay_i = 0.5*self.sigma*Decay[:, None]
+
+        ln_part_1, sign1 = ln_diff_erfs(half_sigma_decay_i + t2_mat/self.sigma, 
+                                        half_sigma_decay_i - inv_sigma_diff_t,
+                                        return_sign=True)
+        ln_part_2, sign2 = ln_diff_erfs(half_sigma_decay_i,
+                                        half_sigma_decay_i - t_mat/self.sigma,
+                                        return_sign=True)
+
+        h = sign1*np.exp(half_sigma_decay_i
+                         *half_sigma_decay_i
+                         -Decay[:, None]*diff_t+ln_part_1
+                         -np.log(Decay[:, None] + Decay2[None, :]))
+        h -= sign2*np.exp(half_sigma_decay_i*half_sigma_decay_i
+                          -Decay[:, None]*t_mat-Decay2[None, :]*t2_mat+ln_part_2
+                          -np.log(Decay[:, None] + Decay2[None, :]))
+
+        if update_derivatives:
+            sigma2 = self.sigma*self.sigma
+            # Update ith decay gradient
+
+            dh_ddecay = ((0.5*Decay[:, None]*sigma2*(Decay[:, None] + Decay2[None, :])-1)*h
+                         + (-diff_t*sign1*np.exp(
+                half_sigma_decay_i*half_sigma_decay_i-Decay[:, None]*diff_t+ln_part_1
+                )
+                            +t_mat*sign2*np.exp(
+                half_sigma_decay_i*half_sigma_decay_i-Decay[:, None]*t_mat
+                - Decay2*t2_mat+ln_part_2))
+                         +self.sigma/np.sqrt(np.pi)*(
+                -np.exp(
+                -diff_t*diff_t/sigma2
+                )+np.exp(
+                -t2_mat*t2_mat/sigma2-Decay[:, None]*t_mat
+                )+np.exp(
+                -t_mat*t_mat/sigma2-Decay2[None, :]*t2_mat
+                )-np.exp(
+                -(Decay[:, None]*t_mat + Decay2[None, :]*t2_mat)
+                )
+                ))
+            self._dh_ddecay = (dh_ddecay/(Decay[:, None]+Decay2[None, :])).real
+            
+            # Update jth decay gradient
+            dh_ddecay2 = (t2_mat*sign2
+                         *np.exp(
+                half_sigma_decay_i*half_sigma_decay_i
+                -(Decay[:, None]*t_mat + Decay2[None, :]*t2_mat)
+                +ln_part_2
+                )
+                         -h)
+            self._dh_ddecay2 = (dh_ddecay/(Decay[:, None] + Decay2[None, :])).real
+            
+            # Update sigma gradient
+            self._dh_dsigma = (half_sigma_decay_i*Decay[:, None]*h
+                               + 2/(np.sqrt(np.pi)
+                                    *(Decay[:, None]+Decay2[None, :]))
+                               *((-diff_t/sigma2-Decay[:, None]/2)
+                                 *np.exp(-diff_t*diff_t/sigma2)
+                                 + (-t2_mat/sigma2+Decay[:, None]/2)
+                                 *np.exp(-t2_mat*t2_mat/sigma2-Decay[:, None]*t_mat) 
+                                 - (-t_mat/sigma2-Decay[:, None]/2) 
+                                 *np.exp(-t_mat*t_mat/sigma2-Decay2[None, :]*t2_mat) 
+                                 - Decay[:, None]/2
+                                 *np.exp(-(Decay[:, None]*t_mat+Decay2[None, :]*t2_mat))))
+                
+        return h

GPy/kern/parts/gibbs.py

@@ -9,7 +9,7 @@ import GPy
 
 class Gibbs(Kernpart):
     """
-    Gibbs and MacKay non-stationary covariance function.
+    Gibbs non-stationary covariance function. 
 
     .. math::
        
@@ -25,7 +25,10 @@ class Gibbs(Kernpart):
         with input location. This leads to an additional term in front of
         the kernel.
 
-        The parameters are :math:`\sigma^2`, the process variance, and the parameters of l(x) which is a function that can be specified by the user, by default an multi-layer peceptron is used is used.
+        The parameters are :math:`\sigma^2`, the process variance, and
+        the parameters of l(x) which is a function that can be
+        specified by the user, by default an multi-layer peceptron is
+        used.
 
         :param input_dim: the number of input dimensions
         :type input_dim: int 
@@ -37,6 +40,15 @@ class Gibbs(Kernpart):
         :type ARD: Boolean
         :rtype: Kernpart object
 
+    See Mark Gibbs's thesis for more details: Gibbs,
+    M. N. (1997). Bayesian Gaussian Processes for Regression and
+    Classification. PhD thesis, Department of Physics, University of
+    Cambridge. Or also see Page 93 of Gaussian Processes for Machine
+    Learning by Rasmussen and Williams. Although note that we do not
+    constrain the lengthscale to be positive by default. This allows
+    anticorrelation to occur. The positive constraint can be included
+    by the user manually.
+
     """
 
     def __init__(self, input_dim, variance=1., mapping=None, ARD=False):
@@ -89,11 +101,17 @@ class Gibbs(Kernpart):
         """Derivative of the covariance matrix with respect to X."""
         # First account for gradients arising from presence of X in exponent.
         self._K_computations(X, X2)
-        _K_dist = X[:, None, :] - X2[None, :, :]
+        if X2 is None:
+            _K_dist = 2*(X[:, None, :] - X[None, :, :])
+        else:
+            _K_dist = X[:, None, :] - X2[None, :, :] # don't cache this in _K_co
         dK_dX = (-2.*self.variance)*np.transpose((self._K_dvar/self._w2)[:, :, None]*_K_dist, (1, 0, 2))
         target += np.sum(dK_dX*dL_dK.T[:, :, None], 0)
         # Now account for gradients arising from presence of X in lengthscale.
         self._dK_computations(dL_dK)
+        if X2 is None:
+            target += 2.*self.mapping.df_dX(self._dL_dl[:, None], X)
+        else:
             target += self.mapping.df_dX(self._dL_dl[:, None], X)
     
     def dKdiag_dX(self, dL_dKdiag, X, target):
@@ -102,7 +120,8 @@ class Gibbs(Kernpart):
 
     def dKdiag_dtheta(self, dL_dKdiag, X, target):
         """Gradient of diagonal of covariance with respect to parameters."""
-        pass
+        target[0] += np.sum(dL_dKdiag)
+
 
     
     def _K_computations(self, X, X2=None):

GPy/kern/parts/hetero.py

@@ -0,0 +1,104 @@
+# Copyright (c) 2013, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+from IPython.core.debugger import Tracer; debug_here=Tracer()
+from kernpart import Kernpart
+import numpy as np
+from ...util.linalg import tdot
+from ...core.mapping import Mapping
+import GPy
+
+class Hetero(Kernpart):
+    """
+    TODO: Need to constrain the function outputs
+    positive (still thinking of best way of doing this!!! Yes, intend to use
+    transformations, but what's the *best* way). Currently just squaring output.
+
+    Heteroschedastic noise which depends on input location. See, for example,
+    this paper by Goldberg et al.
+
+    .. math::
+
+       k(x_i, x_j) = \delta_{i,j} \sigma^2(x_i)
+
+       where :math:`\sigma^2(x)` is a function giving the variance  as a function of input space and :math:`\delta_{i,j}` is the Kronecker delta function.
+
+    The parameters are the parameters of \sigma^2(x) which is a
+    function that can be specified by the user, by default an
+    multi-layer peceptron is used.
+
+    :param input_dim: the number of input dimensions
+    :type input_dim: int
+    :param mapping: the mapping that gives the lengthscale across the input space (by default GPy.mappings.MLP is used with 20 hidden nodes).
+    :type mapping: GPy.core.Mapping
+    :rtype: Kernpart object
+
+    See this paper:
+
+    Goldberg, P. W.  Williams, C. K. I. and Bishop,
+    C. M. (1998) Regression with Input-dependent Noise: a Gaussian
+    Process Treatment In Advances in Neural Information Processing
+    Systems, Volume 10, pp.  493-499. MIT Press
+
+    for a Gaussian process treatment of this problem.
+
+    """
+
+    def __init__(self, input_dim, mapping=None, transform=None):
+        self.input_dim = input_dim
+        if not mapping:
+            mapping = GPy.mappings.MLP(output_dim=1, hidden_dim=20, input_dim=input_dim)
+        if not transform:
+            transform = GPy.core.transformations.logexp()
+
+        self.transform = transform
+        self.mapping = mapping
+        self.name='hetero'
+        self.num_params=self.mapping.num_params
+        self._set_params(self.mapping._get_params())
+
+    def _get_params(self):
+        return self.mapping._get_params()
+
+    def _set_params(self, x):
+        assert x.size == (self.num_params)
+        self.mapping._set_params(x)
+
+    def _get_param_names(self):
+        return self.mapping._get_param_names()
+
+    def K(self, X, X2, target):
+        """Return covariance between X and X2."""
+        if (X2 is None) or (X2 is X):
+            target[np.diag_indices_from(target)] += self._Kdiag(X)
+
+    def Kdiag(self, X, target):
+        """Compute the diagonal of the covariance matrix for X."""
+        target+=self._Kdiag(X)
+
+    def _Kdiag(self, X):
+        """Helper function for computing the diagonal elements of the covariance."""
+        return self.mapping.f(X).flatten()**2
+
+    def dK_dtheta(self, dL_dK, X, X2, target):
+        """Derivative of the covariance with respect to the parameters."""
+        if (X2 is None) or (X2 is X):
+            dL_dKdiag = dL_dK.flat[::dL_dK.shape[0]+1]
+            self.dKdiag_dtheta(dL_dKdiag, X, target)
+
+    def dKdiag_dtheta(self, dL_dKdiag, X, target):
+        """Gradient of diagonal of covariance with respect to parameters."""
+        target += 2.*self.mapping.df_dtheta(dL_dKdiag[:, None]*self.mapping.f(X), X)
+
+    def dK_dX(self, dL_dK, X, X2, target):
+        """Derivative of the covariance matrix with respect to X."""
+        if X2==None or X2 is X:
+            dL_dKdiag = dL_dK.flat[::dL_dK.shape[0]+1]
+            self.dKdiag_dX(dL_dKdiag, X, target)
+
+    def dKdiag_dX(self, dL_dKdiag, X, target):
+        """Gradient of diagonal of covariance with respect to X."""
+        target += 2.*self.mapping.df_dX(dL_dKdiag[:, None], X)*self.mapping.f(X)
+
+
+

GPy/kern/parts/kernpart.py

@@ -58,6 +58,50 @@ class Kernpart(object):
         raise NotImplementedError
     def dK_dX(self, dL_dK, X, X2, target):
         raise NotImplementedError
+    def dKdiag_dX(self, dL_dK, X, target):
+        raise NotImplementedError
+
+
+
+class Kernpart_stationary(Kernpart):
+    def __init__(self, input_dim, lengthscale=None, ARD=False):
+        self.input_dim = input_dim
+        self.ARD = ARD
+        if not ARD:
+            self.num_params = 2
+            if lengthscale is not None:
+                self.lengthscale = np.asarray(lengthscale)
+                assert self.lengthscale.size == 1, "Only one lengthscale needed for non-ARD kernel"
+            else:
+                self.lengthscale = np.ones(1)
+        else:
+            self.num_params = self.input_dim + 1
+            if lengthscale is not None:
+                self.lengthscale = np.asarray(lengthscale)
+                assert self.lengthscale.size == self.input_dim, "bad number of lengthscales"
+            else:
+                self.lengthscale = np.ones(self.input_dim)
+
+        # initialize cache
+        self._Z, self._mu, self._S = np.empty(shape=(3, 1))
+        self._X, self._X2, self._params = np.empty(shape=(3, 1))
+
+    def _set_params(self, x):
+        self.lengthscale = x
+        self.lengthscale2 = np.square(self.lengthscale)
+        # reset cached results
+        self._X, self._X2, self._params = np.empty(shape=(3, 1))
+        self._Z, self._mu, self._S = np.empty(shape=(3, 1)) # cached versions of Z,mu,S
+
+
+    def dKdiag_dtheta(self, dL_dKdiag, X, target):
+        # For stationary covariances, derivative of diagonal elements
+        # wrt lengthscale is 0.
+        target[0] += np.sum(dL_dKdiag)
+
+    def dKdiag_dX(self, dL_dK, X, target):
+        pass # true for all stationary kernels
+
 
 class Kernpart_inner(Kernpart):
     def __init__(self,input_dim):
@@ -74,3 +118,5 @@ class Kernpart_inner(Kernpart):
         # initialize cache
         self._Z, self._mu, self._S = np.empty(shape=(3, 1))
         self._X, self._X2, self._params = np.empty(shape=(3, 1))
+
+

GPy/kern/parts/linear.py

@@ -99,6 +99,9 @@ class Linear(Kernpart):
             target += tmp.sum()
 
     def dK_dX(self, dL_dK, X, X2, target):
+        if X2 is None:
+            target += 2*(((X[None,:, :] * self.variances)) * dL_dK[:, :, None]).sum(1)
+        else:
             target += (((X2[None,:, :] * self.variances)) * dL_dK[:, :, None]).sum(1)
 
     def dKdiag_dX(self,dL_dKdiag,X,target):

GPy/kern/parts/mlp.py

@@ -7,11 +7,13 @@ four_over_tau = 2./np.pi
 
 class MLP(Kernpart):
     """
-    multi layer perceptron kernel (also known as arc sine kernel or neural network kernel)
+
+    Multi layer perceptron kernel (also known as arc sine kernel or neural network kernel)
 
     .. math::
 
-       k(x,y) = \sigma^2 \frac{2}{\pi}  \text{asin} \left(\frac{\sigma_w^2 x^\top y+\sigma_b^2}{\sqrt{\sigma_w^2x^\top x + \sigma_b^2 + 1}\sqrt{\sigma_w^2 y^\top y \sigma_b^2 +1}} \right)
+          k(x,y) = \\sigma^{2}\\frac{2}{\\pi }  \\text{asin} \\left ( \\frac{ \\sigma_w^2 x^\\top y+\\sigma_b^2}{\\sqrt{\\sigma_w^2x^\\top x + \\sigma_b^2 + 1}\\sqrt{\\sigma_w^2 y^\\top y \\sigma_b^2 +1}} \\right )
+          
 
     :param input_dim: the number of input dimensions
     :type input_dim: int 
@@ -24,6 +26,7 @@ class MLP(Kernpart):
     :type ARD: Boolean
     :rtype: Kernpart object
 
+
     """
 
     def __init__(self, input_dim, variance=1., weight_variance=None, bias_variance=100., ARD=False):
@@ -110,9 +113,13 @@ class MLP(Kernpart):
         arg = self._K_asin_arg
         numer = self._K_numer
         denom = self._K_denom
-        vec2 = (X2*X2).sum(1)*self.weight_variance + self.bias_variance + 1.
         denom3 = denom*denom*denom
+        if X2 is not None:
+            vec2 = (X2*X2).sum(1)*self.weight_variance+self.bias_variance + 1.
             target += four_over_tau*self.weight_variance*self.variance*((X2[None, :, :]/denom[:, :, None] - vec2[None, :, None]*X[:, None, :]*(numer/denom3)[:, :, None])*(dL_dK/np.sqrt(1-arg*arg))[:, :, None]).sum(1)
+        else:
+            vec = (X*X).sum(1)*self.weight_variance+self.bias_variance + 1.
+            target += 2*four_over_tau*self.weight_variance*self.variance*((X[None, :, :]/denom[:, :, None] - vec[None, :, None]*X[:, None, :]*(numer/denom3)[:, :, None])*(dL_dK/np.sqrt(1-arg*arg))[:, :, None]).sum(1)
             
     def dKdiag_dX(self, dL_dKdiag, X, target):
         """Gradient of diagonal of covariance with respect to X"""

GPy/kern/parts/odekern1.c

@@ -0,0 +1,38 @@
+#include <math.h> 
+
+ double k_uu(t1,t2,theta1,theta2,sig1,sig2)
+ {
+  double kern=0;
+  double dist=0;
+  
+  dist = sqrt(t2*t2-t1*t1) 
+ 
+  kern = sig1*(1+theta1*dist)*exp(-theta1*dist)
+
+ return kern;
+ }
+
+
+
+ double k_yy(t1, t2, theta1,theta2,sig1,sig2)
+ {
+  double kern=0;
+  double dist=0;
+  
+  dist = sqrt(t2*t2-t1*t1) 
+ 
+  kern = sig1*sig2 * (  exp(-theta1*dist)*(theta2-2*theta1+theta1*theta2*dist-theta1*theta1*dist) +
+  	exp(-dist)  ) / ((theta2-theta1)*(theta2-theta1))
+
+  return kern;
+ } 
+
+
+
+
+
+
+	
+
+
+

GPy/kern/parts/poly.py

@@ -7,22 +7,22 @@ four_over_tau = 2./np.pi
 
 class POLY(Kernpart):
     """
-    polynomial kernel parameter initialisation.  Included for completeness, but generally not recommended, is the polynomial kernel,
+
+    Polynomial kernel parameter initialisation.  Included for completeness, but generally not recommended, is the polynomial kernel:
+
     .. math::
+        k(x, y) = \sigma^2\*(\sigma_w^2 x'y+\sigma_b^b)^d
 
-    k(x, y) = \sigma^2*(\sigma_w^2 x'y+\sigma_b^b)^d
+    The kernel parameters are :math:`\sigma^2` (variance), :math:`\sigma^2_w`
-
+    (weight_variance), :math:`\sigma^2_b` (bias_variance) and d
-    The kernel parameters are \sigma^2 (variance), \sigma^2_w
-    (weight_variance), \sigma^2_b (bias_variance) and d
     (degree). Only gradients of the first three are provided for
     kernel optimisation, it is assumed that polynomial degree would
     be set by hand.
 
     The kernel is not recommended as it is badly behaved when the
-    \sigma^2_w*x'*y + \sigma^2_b has a magnitude greater than one. For completeness
+    :math:`\sigma^2_w\*x'\*y + \sigma^2_b` has a magnitude greater than one. For completeness
     there is an automatic relevance determination version of this
-    kernel provided.
+    kernel provided (NOTE YET IMPLEMENTED!).
-
     :param input_dim: the number of input dimensions
     :type input_dim: int 
     :param variance: the variance :math:`\sigma^2`
@@ -32,7 +32,7 @@ class POLY(Kernpart):
     :param bias_variance: the variance of the prior over bias parameters :math:`\sigma^2_b`
     :param degree: the degree of the polynomial.
     :type degree: int
-    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter \sigma^2_w), otherwise there is one weight variance parameter per dimension.
+    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter :math:`\sigma^2_w`), otherwise there is one weight variance parameter per dimension.
     :type ARD: Boolean
     :rtype: Kernpart object
 
@@ -103,6 +103,9 @@ class POLY(Kernpart):
         """Derivative of the covariance matrix with respect to X"""
         self._K_computations(X, X2)
         arg = self._K_poly_arg
+        if X2 is None:
+            target += 2*self.weight_variance*self.degree*self.variance*(((X[None,:, :])) *(arg**(self.degree-1))[:, :, None]*dL_dK[:, :, None]).sum(1)
+        else:
             target += self.weight_variance*self.degree*self.variance*(((X2[None,:, :])) *(arg**(self.degree-1))[:, :, None]*dL_dK[:, :, None]).sum(1)
             
     def dKdiag_dX(self, dL_dKdiag, X, target):

GPy/kern/parts/prod.py

@@ -2,6 +2,7 @@
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
 from kernpart import Kernpart
+from coregionalize import Coregionalize
 import numpy as np
 import hashlib
 
@@ -18,7 +19,7 @@ class Prod(Kernpart):
     """
     def __init__(self,k1,k2,tensor=False):
         self.num_params = k1.num_params + k2.num_params
-        self.name = k1.name + '<times>' + k2.name
+        self.name = '['+k1.name + '**' + k2.name +']'
         self.k1 = k1
         self.k2 = k2
         if tensor:
@@ -90,6 +91,16 @@ class Prod(Kernpart):
     def dK_dX(self,dL_dK,X,X2,target):
         """derivative of the covariance matrix with respect to X."""
         self._K_computations(X,X2)
+        if X2 is None:
+            if not isinstance(self.k1,Coregionalize) and not isinstance(self.k2,Coregionalize):
+                self.k1.dK_dX(dL_dK*self._K2, X[:,self.slice1], None, target[:,self.slice1])
+                self.k2.dK_dX(dL_dK*self._K1, X[:,self.slice2], None, target[:,self.slice2])
+            else:#if isinstance(self.k1,Coregionalize) or isinstance(self.k2,Coregionalize):
+                #NOTE The indices column in the inputs makes the ki.dK_dX fail when passing None instead of X[:,self.slicei]
+                X2 = X
+                self.k1.dK_dX(2.*dL_dK*self._K2, X[:,self.slice1], X2[:,self.slice1], target[:,self.slice1])
+                self.k2.dK_dX(2.*dL_dK*self._K1, X[:,self.slice2], X2[:,self.slice2], target[:,self.slice2])
+        else:
             self.k1.dK_dX(dL_dK*self._K2, X[:,self.slice1], X2[:,self.slice1], target[:,self.slice1])
             self.k2.dK_dX(dL_dK*self._K1, X[:,self.slice2], X2[:,self.slice2], target[:,self.slice2])
 

GPy/kern/parts/rational_quadratic.py

@@ -57,7 +57,7 @@ class RationalQuadratic(Kernpart):
         dist2 = np.square((X-X2.T)/self.lengthscale)
 
         dvar = (1 + dist2/2.)**(-self.power)
-        dl = self.power * self.variance * dist2 * self.lengthscale**(-3) * (1 + dist2/2./self.power)**(-self.power-1)
+        dl = self.power * self.variance * dist2 / self.lengthscale * (1 + dist2/2.)**(-self.power-1)
         dp = - self.variance * np.log(1 + dist2/2.) * (1 + dist2/2.)**(-self.power)
 
         target[0] += np.sum(dvar*dL_dK)
@@ -70,9 +70,11 @@ class RationalQuadratic(Kernpart):
 
     def dK_dX(self,dL_dK,X,X2,target):
         """derivative of the covariance matrix with respect to X."""
-        if X2 is None: X2 = X
+        if X2 is None:
+            dist2 = np.square((X-X.T)/self.lengthscale)
+            dX = -2.*self.variance*self.power * (X-X.T)/self.lengthscale**2 *  (1 + dist2/2./self.lengthscale)**(-self.power-1)
+        else:
             dist2 = np.square((X-X2.T)/self.lengthscale)
-
             dX = -self.variance*self.power * (X-X2.T)/self.lengthscale**2 *  (1 + dist2/2./self.lengthscale)**(-self.power-1)
         target += np.sum(dL_dK*dX,1)[:,np.newaxis]
 

GPy/kern/parts/rbf.py

@@ -138,6 +138,9 @@ class RBF(Kernpart):
 
     def dK_dX(self, dL_dK, X, X2, target):
         self._K_computations(X, X2)
+        if X2 is None:
+            _K_dist = 2*(X[:, None, :] - X[None, :, :])
+        else:
             _K_dist = X[:, None, :] - X2[None, :, :] # don't cache this in _K_computations because it is high memory. If this function is being called, chances are we're not in the high memory arena.
         dK_dX = (-self.variance / self.lengthscale2) * np.transpose(self._K_dvar[:, :, np.newaxis] * _K_dist, (1, 0, 2))
         target += np.sum(dK_dX * dL_dK.T[:, :, None], 0)

GPy/kern/parts/rbf_inv.py

@@ -133,6 +133,9 @@ class RBFInv(RBF):
 
     def dK_dX(self, dL_dK, X, X2, target):
         self._K_computations(X, X2)
+        if X2 is None:            
+            _K_dist = 2*(X[:, None, :] - X[None, :, :])
+        else:
             _K_dist = X[:, None, :] - X2[None, :, :] # don't cache this in _K_computations because it is high memory. If this function is being called, chances are we're not in the high memory arena.
         dK_dX = (-self.variance * self.inv_lengthscale2) * np.transpose(self._K_dvar[:, :, np.newaxis] * _K_dist, (1, 0, 2))
         target += np.sum(dK_dX * dL_dK.T[:, :, None], 0)

GPy/kern/parts/sympy_helpers.cpp

@@ -1,6 +1,7 @@
 #include <math.h>
 double DiracDelta(double x){
-    if((x<0.000001) & (x>-0.000001))//go on, laught at my c++ skills
+  // TODO: this doesn't seem to be a dirac delta ... should return infinity. Neil
+    if((x<0.000001) & (x>-0.000001))//go on, laugh at my c++ skills
         return 1.0;
     else
         return 0.0;
@@ -8,3 +9,17 @@ double DiracDelta(double x){
 double DiracDelta(double x,int foo){
     return 0.0;
 };
+
+double sinc(double x){
+  if (x==0)
+    return 1.0;
+  else 
+    return sin(x)/x;
+}
+
+double sinc_grad(double x){
+  if (x==0)
+    return 0.0;
+  else 
+    return (x*cos(x) - sin(x))/(x*x);
+}

GPy/kern/parts/sympy_helpers.h

@@ -1,3 +1,6 @@
 #include <math.h>
 double DiracDelta(double x);
 double DiracDelta(double x, int foo);
+
+double sinc(double x);
+double sinc_grad(double x);

GPy/kern/parts/sympykern.py

@@ -26,8 +26,11 @@ class spkern(Kernpart):
      - to handle multiple inputs, call them x1, z1, etc
      - to handle multpile correlated outputs, you'll need to define each covariance function and 'cross' variance function. TODO
     """
-    def __init__(self,input_dim,k,param=None):
+    def __init__(self,input_dim,k,name=None,param=None):
+        if name is None:
             self.name='sympykern'
+        else:
+            self.name = name
         self._sp_k = k
         sp_vars = [e for e in k.atoms() if e.is_Symbol]
         self._sp_x= sorted([e for e in sp_vars if e.name[0]=='x'],key=lambda x:int(x.name[1:]))
@@ -56,9 +59,9 @@ class spkern(Kernpart):
 
         self.weave_kwargs = {\
             'support_code':self._function_code,\
-            'include_dirs':[tempfile.gettempdir(), os.path.join(current_dir,'kern/')],\
+            'include_dirs':[tempfile.gettempdir(), os.path.join(current_dir,'parts/')],\
             'headers':['"sympy_helpers.h"'],\
-            'sources':[os.path.join(current_dir,"kern/sympy_helpers.cpp")],\
+            'sources':[os.path.join(current_dir,"parts/sympy_helpers.cpp")],\
             #'extra_compile_args':['-ftree-vectorize', '-mssse3', '-ftree-vectorizer-verbose=5'],\
             'extra_compile_args':[],\
             'extra_link_args':['-lgomp'],\
@@ -109,14 +112,15 @@ class spkern(Kernpart):
         f.write(self._function_header)
         f.close()
 
-        #get rid of derivatives of DiracDelta
+        # Substitute any known derivatives which sympy doesn't compute
         self._function_code = re.sub('DiracDelta\(.+?,.+?\)','0.0',self._function_code)
 
-        #Here's some code to do the looping for K
+        # Here's the code to do the looping for K
-        arglist = ", ".join(["X[i*input_dim+%s]"%x.name[1:] for x in self._sp_x]\
+        arglist = ", ".join(["X[i*input_dim+%s]"%x.name[1:] for x in self._sp_x]
-                + ["Z[j*input_dim+%s]"%z.name[1:] for z in self._sp_z]\
+                            + ["Z[j*input_dim+%s]"%z.name[1:] for z in self._sp_z]
                             + ["param[%i]"%i for i in range(self.num_params)])
 
+        
         self._K_code =\
         """
         int i;
@@ -133,9 +137,14 @@ class spkern(Kernpart):
         %s
         """%(arglist,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
 
+        # Similar code when only X is provided. 
+        self._K_code_X = self._K_code.replace('Z[', 'X[')
+
+        
+        # Code to compute diagonal of covariance.
         diag_arglist = re.sub('Z','X',arglist)
         diag_arglist = re.sub('j','i',diag_arglist)
-        #Here's some code to do the looping for Kdiag
+        # Code to do the looping for Kdiag
         self._Kdiag_code =\
         """
         int i;
@@ -148,8 +157,9 @@ class spkern(Kernpart):
         %s
         """%(diag_arglist,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
 
-        #here's some code to compute gradients
+        # Code to compute gradients
         funclist = '\n'.join([' '*16 + 'target[%i] += partial[i*num_inducing+j]*dk_d%s(%s);'%(i,theta.name,arglist) for i,theta in  enumerate(self._sp_theta)])
+
         self._dK_dtheta_code =\
         """
         int i;
@@ -164,9 +174,12 @@ class spkern(Kernpart):
             }
         }
         %s
-        """%(funclist,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
+        """%(funclist,"/*"+str(self._sp_k)+"*/") # adding a string representation forces recompile when needed
 
-        #here's some code to compute gradients for Kdiag TODO: thius is yucky.
+        # Similar code when only X is provided, change argument lists.
+        self._dK_dtheta_code_X = self._dK_dtheta_code.replace('Z[', 'X[')
+
+        # Code to compute gradients for Kdiag TODO: needs clean up
         diag_funclist = re.sub('Z','X',funclist,count=0)
         diag_funclist = re.sub('j','i',diag_funclist)
         diag_funclist = re.sub('partial\[i\*num_inducing\+i\]','partial[i]',diag_funclist)
@@ -181,8 +194,12 @@ class spkern(Kernpart):
         %s
         """%(diag_funclist,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
 
-        #Here's some code to do gradients wrt x
+        # Code for gradients wrt X
         gradient_funcs = "\n".join(["target[i*input_dim+%i] += partial[i*num_inducing+j]*dk_dx%i(%s);"%(q,q,arglist) for q in range(self.input_dim)])
+        if False:
+            gradient_funcs += """if(isnan(target[i*input_dim+2])){printf("%%f\\n",dk_dx2(X[i*input_dim+0], X[i*input_dim+1], X[i*input_dim+2], Z[j*input_dim+0], Z[j*input_dim+1], Z[j*input_dim+2], param[0], param[1], param[2], param[3], param[4], param[5]));}
+            if(isnan(target[i*input_dim+2])){printf("%%f,%%f,%%i,%%i\\n", X[i*input_dim+2], Z[j*input_dim+2],i,j);}"""
+
         self._dK_dX_code = \
         """
         int i;
@@ -194,28 +211,32 @@ class spkern(Kernpart):
         for (i=0;i<N; i++){
           for (j=0; j<num_inducing; j++){
             %s
-                //if(isnan(target[i*input_dim+2])){printf("%%f\\n",dk_dx2(X[i*input_dim+0], X[i*input_dim+1], X[i*input_dim+2], Z[j*input_dim+0], Z[j*input_dim+1], Z[j*input_dim+2], param[0], param[1], param[2], param[3], param[4], param[5]));}
-                //if(isnan(target[i*input_dim+2])){printf("%%f,%%f,%%i,%%i\\n", X[i*input_dim+2], Z[j*input_dim+2],i,j);}
-
           }
         }
         %s
         """%(gradient_funcs,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
   
-        #now for gradients of Kdiag wrt X
+        # Create code for call when just X is passed as argument.
+        self._dK_dX_code_X = self._dK_dX_code.replace('Z[', 'X[').replace('+= partial[', '+= 2*partial[')
+
+        diag_gradient_funcs = re.sub('Z','X',gradient_funcs,count=0)
+        diag_gradient_funcs = re.sub('j','i',diag_gradient_funcs)
+        diag_gradient_funcs = re.sub('partial\[i\*num_inducing\+i\]','2*partial[i]',diag_gradient_funcs)
+
+        # Code for gradients of Kdiag wrt X
         self._dKdiag_dX_code= \
         """
-        int i;
-        int j;
         int N = partial_array->dimensions[0];
-        int num_inducing = 0;
         int input_dim = X_array->dimensions[1];
-        for (i=0;i<N; i++){
+        for (int i=0;i<N; i++){
-            j = i;
             %s
         }
         %s
-        """%(gradient_funcs,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
+        """%(diag_gradient_funcs,"/*"+str(self._sp_k)+"*/") #adding a
+        # string representation forces recompile when needed Get rid
+        # of Zs in argument for diagonal. TODO: Why wasn't
+        # diag_funclist called here? Need to check that.
+        #self._dKdiag_dX_code = self._dKdiag_dX_code.replace('Z[j', 'X[i')
 
 
         #TODO: insert multiple functions here via string manipulation
@@ -223,6 +244,9 @@ class spkern(Kernpart):
 
     def K(self,X,Z,target):
         param = self._param
+        if Z is None:
+            weave.inline(self._K_code_X,arg_names=['target','X','param'],**self.weave_kwargs)
+        else:
             weave.inline(self._K_code,arg_names=['target','X','Z','param'],**self.weave_kwargs)
 
     def Kdiag(self,X,target):
@@ -231,21 +255,25 @@ class spkern(Kernpart):
 
     def dK_dtheta(self,partial,X,Z,target):
         param = self._param
-        weave.inline(self._dK_dtheta_code,arg_names=['target','X','Z','param','partial'],**self.weave_kwargs)
+        if Z is None:
+            weave.inline(self._dK_dtheta_code_X, arg_names=['target','X','param','partial'],**self.weave_kwargs)
+        else:
+            weave.inline(self._dK_dtheta_code, arg_names=['target','X','Z','param','partial'],**self.weave_kwargs)
 
     def dKdiag_dtheta(self,partial,X,target):
         param = self._param
-        Z = X
+        weave.inline(self._dKdiag_dtheta_code,arg_names=['target','X','param','partial'],**self.weave_kwargs)
-        weave.inline(self._dKdiag_dtheta_code,arg_names=['target','X','Z','param','partial'],**self.weave_kwargs)
 
     def dK_dX(self,partial,X,Z,target):
         param = self._param
+        if Z is None:
+            weave.inline(self._dK_dX_code_X,arg_names=['target','X','param','partial'],**self.weave_kwargs)
+        else:
             weave.inline(self._dK_dX_code,arg_names=['target','X','Z','param','partial'],**self.weave_kwargs)
 
     def dKdiag_dX(self,partial,X,target):
         param = self._param
-        Z = X
+        weave.inline(self._dKdiag_dX_code,arg_names=['target','X','param','partial'],**self.weave_kwargs)
-        weave.inline(self._dKdiag_dX_code,arg_names=['target','X','Z','param','partial'],**self.weave_kwargs)
 
     def _set_params(self,param):
         #print param.flags['C_CONTIGUOUS']

GPy/likelihoods/__init__.py

@@ -1,5 +1,6 @@
 from ep import EP
 from laplace import Laplace
+from ep_mixed_noise import EP_Mixed_Noise
 from gaussian import Gaussian
-# TODO: from Laplace import Laplace
+from gaussian_mixed_noise import Gaussian_Mixed_Noise
-import likelihood_functions as functions
+from noise_model_constructors import *

GPy/likelihoods/ep.py

@@ -4,45 +4,46 @@ from ..util.linalg import pdinv,mdot,jitchol,chol_inv,DSYR,tdot,dtrtrs
 from likelihood import likelihood
 
 class EP(likelihood):
-    def __init__(self,data,LikelihoodFunction,epsilon=1e-3,power_ep=[1.,1.]):
+    def __init__(self,data,noise_model):
         """
         Expectation Propagation
 
-        Arguments
+        :param data: data to model
-        ---------
+        :type data: numpy array
-        epsilon : Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float)
+        :param noise_model: noise distribution
-        LikelihoodFunction : a likelihood function (see likelihood_functions.py)
+        :type noise_model: A GPy noise model
+
         """
-        self.LikelihoodFunction = LikelihoodFunction
+        self.noise_model = noise_model
-        self.epsilon = epsilon
-        self.eta, self.delta = power_ep
         self.data = data
-        self.N, self.output_dim = self.data.shape
+        self.num_data, self.output_dim = self.data.shape
         self.is_heteroscedastic = True
         self.Nparams = 0
-        self._transf_data = self.LikelihoodFunction._preprocess_values(data)
+        self._transf_data = self.noise_model._preprocess_values(data)
 
         #Initial values - Likelihood approximation parameters:
         #p(y|f) = t(f|tau_tilde,v_tilde)
-        self.tau_tilde = np.zeros(self.N)
+        self.tau_tilde = np.zeros(self.num_data)
-        self.v_tilde = np.zeros(self.N)
+        self.v_tilde = np.zeros(self.num_data)
 
         #initial values for the GP variables
-        self.Y = np.zeros((self.N,1))
+        self.Y = np.zeros((self.num_data,1))
-        self.covariance_matrix = np.eye(self.N)
+        self.covariance_matrix = np.eye(self.num_data)
-        self.precision = np.ones(self.N)[:,None]
+        self.precision = np.ones(self.num_data)[:,None]
         self.Z = 0
         self.YYT = None
         self.V = self.precision * self.Y
         self.VVT_factor = self.V
         self.trYYT = 0.
 
+        super(EP, self).__init__()
+
     def restart(self):
-        self.tau_tilde = np.zeros(self.N)
+        self.tau_tilde = np.zeros(self.num_data)
-        self.v_tilde = np.zeros(self.N)
+        self.v_tilde = np.zeros(self.num_data)
-        self.Y = np.zeros((self.N,1))
+        self.Y = np.zeros((self.num_data,1))
-        self.covariance_matrix = np.eye(self.N)
+        self.covariance_matrix = np.eye(self.num_data)
-        self.precision = np.ones(self.N)[:,None]
+        self.precision = np.ones(self.num_data)[:,None]
         self.Z = 0
         self.YYT = None
         self.V = self.precision * self.Y
@@ -52,16 +53,23 @@ class EP(likelihood):
     def predictive_values(self,mu,var,full_cov):
         if full_cov:
             raise NotImplementedError, "Cannot make correlated predictions with an EP likelihood"
-        return self.LikelihoodFunction.predictive_values(mu,var)
+        return self.noise_model.predictive_values(mu,var)
 
     def _get_params(self):
-        return np.zeros(0)
+        #return np.zeros(0)
+        return self.noise_model._get_params()
+
     def _get_param_names(self):
-        return []
+        #return []
+        return self.noise_model._get_param_names()
+
     def _set_params(self,p):
-        pass # TODO: the EP likelihood might want to take some parameters...
+        #pass # TODO: the EP likelihood might want to take some parameters...
+        self.noise_model._set_params(p)
+
     def _gradients(self,partial):
-        return np.zeros(0) # TODO: the EP likelihood might want to take some parameters...
+        #return np.zeros(0) # TODO: the EP likelihood might want to take some parameters...
+        return self.noise_model._gradients(partial)
 
     def _compute_GP_variables(self):
         #Variables to be called from GP
@@ -69,6 +77,7 @@ class EP(likelihood):
         sigma_sum = 1./self.tau_ + 1./self.tau_tilde
         mu_diff_2 = (self.v_/self.tau_ - mu_tilde)**2
         self.Z = np.sum(np.log(self.Z_hat)) + 0.5*np.sum(np.log(sigma_sum)) + 0.5*np.sum(mu_diff_2/sigma_sum) #Normalization constant, aka Z_ep
+        self.Z += 0.5*self.num_data*np.log(2*np.pi)
 
         self.Y =  mu_tilde[:,None]
         self.YYT = np.dot(self.Y,self.Y.T)
@@ -78,13 +87,22 @@ class EP(likelihood):
         self.VVT_factor = self.V
         self.trYYT = np.trace(self.YYT)
 
-    def fit_full(self,K):
+    def fit_full(self, K, epsilon=1e-3,power_ep=[1.,1.]):
         """
         The expectation-propagation algorithm.
         For nomenclature see Rasmussen & Williams 2006.
+
+        :param epsilon: Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float)
+        :type epsilon: float
+        :param power_ep: Power EP parameters
+        :type power_ep: list of floats
+
         """
+        self.epsilon = epsilon
+        self.eta, self.delta = power_ep
+
         #Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma)
-        mu = np.zeros(self.N)
+        mu = np.zeros(self.num_data)
         Sigma = K.copy()
 
         """
@@ -93,15 +111,15 @@ class EP(likelihood):
         sigma_ = 1./tau_
         mu_ = v_/tau_
         """
-        self.tau_ = np.empty(self.N,dtype=float)
+        self.tau_ = np.empty(self.num_data,dtype=float)
-        self.v_ = np.empty(self.N,dtype=float)
+        self.v_ = np.empty(self.num_data,dtype=float)
 
         #Initial values - Marginal moments
-        z = np.empty(self.N,dtype=float)
+        z = np.empty(self.num_data,dtype=float)
-        self.Z_hat = np.empty(self.N,dtype=float)
+        self.Z_hat = np.empty(self.num_data,dtype=float)
-        phi = np.empty(self.N,dtype=float)
+        phi = np.empty(self.num_data,dtype=float)
-        mu_hat = np.empty(self.N,dtype=float)
+        mu_hat = np.empty(self.num_data,dtype=float)
-        sigma2_hat = np.empty(self.N,dtype=float)
+        sigma2_hat = np.empty(self.num_data,dtype=float)
 
         #Approximation
         epsilon_np1 = self.epsilon + 1.
@@ -110,13 +128,13 @@ class EP(likelihood):
         self.np1 = [self.tau_tilde.copy()]
         self.np2 = [self.v_tilde.copy()]
         while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon:
-            update_order = np.random.permutation(self.N)
+            update_order = np.random.permutation(self.num_data)
             for i in update_order:
                 #Cavity distribution parameters
                 self.tau_[i] = 1./Sigma[i,i] - self.eta*self.tau_tilde[i]
                 self.v_[i] = mu[i]/Sigma[i,i] - self.eta*self.v_tilde[i]
                 #Marginal moments
-                self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.LikelihoodFunction.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
+                self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
                 #Site parameters update
                 Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma[i,i])
                 Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma[i,i])
@@ -128,23 +146,32 @@ class EP(likelihood):
                 self.iterations += 1
             #Sigma recomptutation with Cholesky decompositon
             Sroot_tilde_K = np.sqrt(self.tau_tilde)[:,None]*K
-            B = np.eye(self.N) + np.sqrt(self.tau_tilde)[None,:]*Sroot_tilde_K
+            B = np.eye(self.num_data) + np.sqrt(self.tau_tilde)[None,:]*Sroot_tilde_K
             L = jitchol(B)
             V,info = dtrtrs(L,Sroot_tilde_K,lower=1)
             Sigma = K - np.dot(V.T,V)
             mu = np.dot(Sigma,self.v_tilde)
-            epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.N
+            epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.num_data
-            epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.N
+            epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.num_data
             self.np1.append(self.tau_tilde.copy())
             self.np2.append(self.v_tilde.copy())
 
         return self._compute_GP_variables()
 
-    def fit_DTC(self, Kmm, Kmn):
+    def fit_DTC(self, Kmm, Kmn, epsilon=1e-3,power_ep=[1.,1.]):
         """
         The expectation-propagation algorithm with sparse pseudo-input.
         For nomenclature see ... 2013.
+
+        :param epsilon: Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float)
+        :type epsilon: float
+        :param power_ep: Power EP parameters
+        :type power_ep: list of floats
+
         """
+        self.epsilon = epsilon
+        self.eta, self.delta = power_ep
+
         num_inducing = Kmm.shape[0]
 
         #TODO: this doesn't work with uncertain inputs!
@@ -173,7 +200,7 @@ class EP(likelihood):
         Sigma = Diag + P*R.T*R*P.T + K
         mu = w + P*Gamma
         """
-        mu = np.zeros(self.N)
+        mu = np.zeros(self.num_data)
         LLT = Kmm.copy()
         Sigma_diag = Qnn_diag.copy()
 
@@ -183,15 +210,15 @@ class EP(likelihood):
         sigma_ = 1./tau_
         mu_ = v_/tau_
         """
-        self.tau_ = np.empty(self.N,dtype=float)
+        self.tau_ = np.empty(self.num_data,dtype=float)
-        self.v_ = np.empty(self.N,dtype=float)
+        self.v_ = np.empty(self.num_data,dtype=float)
 
         #Initial values - Marginal moments
-        z = np.empty(self.N,dtype=float)
+        z = np.empty(self.num_data,dtype=float)
-        self.Z_hat = np.empty(self.N,dtype=float)
+        self.Z_hat = np.empty(self.num_data,dtype=float)
-        phi = np.empty(self.N,dtype=float)
+        phi = np.empty(self.num_data,dtype=float)
-        mu_hat = np.empty(self.N,dtype=float)
+        mu_hat = np.empty(self.num_data,dtype=float)
-        sigma2_hat = np.empty(self.N,dtype=float)
+        sigma2_hat = np.empty(self.num_data,dtype=float)
 
         #Approximation
         epsilon_np1 = 1
@@ -200,13 +227,13 @@ class EP(likelihood):
         np1 = [self.tau_tilde.copy()]
         np2 = [self.v_tilde.copy()]
         while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon:
-            update_order = np.random.permutation(self.N)
+            update_order = np.random.permutation(self.num_data)
             for i in update_order:
                 #Cavity distribution parameters
                 self.tau_[i] = 1./Sigma_diag[i] - self.eta*self.tau_tilde[i]
                 self.v_[i] = mu[i]/Sigma_diag[i] - self.eta*self.v_tilde[i]
                 #Marginal moments
-                self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.LikelihoodFunction.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
+                self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
                 #Site parameters update
                 Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i])
                 Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i])
@@ -229,18 +256,26 @@ class EP(likelihood):
             Sigma_diag = np.sum(V*V,-2)
             Knmv_tilde = np.dot(Kmn,self.v_tilde)
             mu = np.dot(V2.T,Knmv_tilde)
-            epsilon_np1 = sum((self.tau_tilde-np1[-1])**2)/self.N
+            epsilon_np1 = sum((self.tau_tilde-np1[-1])**2)/self.num_data
-            epsilon_np2 = sum((self.v_tilde-np2[-1])**2)/self.N
+            epsilon_np2 = sum((self.v_tilde-np2[-1])**2)/self.num_data
             np1.append(self.tau_tilde.copy())
             np2.append(self.v_tilde.copy())
 
         self._compute_GP_variables()
 
-    def fit_FITC(self, Kmm, Kmn, Knn_diag):
+    def fit_FITC(self, Kmm, Kmn, Knn_diag, epsilon=1e-3,power_ep=[1.,1.]):
         """
         The expectation-propagation algorithm with sparse pseudo-input.
         For nomenclature see Naish-Guzman and Holden, 2008.
+
+        :param epsilon: Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float)
+        :type epsilon: float
+        :param power_ep: Power EP parameters
+        :type power_ep: list of floats
         """
+        self.epsilon = epsilon
+        self.eta, self.delta = power_ep
+
         num_inducing = Kmm.shape[0]
 
         """
@@ -263,9 +298,9 @@ class EP(likelihood):
         Sigma = Diag + P*R.T*R*P.T + K
         mu = w + P*Gamma
         """
-        self.w = np.zeros(self.N)
+        self.w = np.zeros(self.num_data)
         self.Gamma = np.zeros(num_inducing)
-        mu = np.zeros(self.N)
+        mu = np.zeros(self.num_data)
         P = P0.copy()
         R = R0.copy()
         Diag = Diag0.copy()
@@ -278,15 +313,15 @@ class EP(likelihood):
         sigma_ = 1./tau_
         mu_ = v_/tau_
         """
-        self.tau_ = np.empty(self.N,dtype=float)
+        self.tau_ = np.empty(self.num_data,dtype=float)
-        self.v_ = np.empty(self.N,dtype=float)
+        self.v_ = np.empty(self.num_data,dtype=float)
 
         #Initial values - Marginal moments
-        z = np.empty(self.N,dtype=float)
+        z = np.empty(self.num_data,dtype=float)
-        self.Z_hat = np.empty(self.N,dtype=float)
+        self.Z_hat = np.empty(self.num_data,dtype=float)
-        phi = np.empty(self.N,dtype=float)
+        phi = np.empty(self.num_data,dtype=float)
-        mu_hat = np.empty(self.N,dtype=float)
+        mu_hat = np.empty(self.num_data,dtype=float)
-        sigma2_hat = np.empty(self.N,dtype=float)
+        sigma2_hat = np.empty(self.num_data,dtype=float)
 
         #Approximation
         epsilon_np1 = 1
@@ -295,13 +330,13 @@ class EP(likelihood):
         self.np1 = [self.tau_tilde.copy()]
         self.np2 = [self.v_tilde.copy()]
         while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon:
-            update_order = np.random.permutation(self.N)
+            update_order = np.random.permutation(self.num_data)
             for i in update_order:
                 #Cavity distribution parameters
                 self.tau_[i] = 1./Sigma_diag[i] - self.eta*self.tau_tilde[i]
                 self.v_[i] = mu[i]/Sigma_diag[i] - self.eta*self.v_tilde[i]
                 #Marginal moments
-                self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.LikelihoodFunction.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
+                self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
                 #Site parameters update
                 Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i])
                 Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i])
@@ -334,8 +369,8 @@ class EP(likelihood):
             self.w = Diag * self.v_tilde
             self.Gamma = np.dot(R.T, np.dot(RPT,self.v_tilde))
             mu = self.w + np.dot(P,self.Gamma)
-            epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.N
+            epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.num_data
-            epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.N
+            epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.num_data
             self.np1.append(self.tau_tilde.copy())
             self.np2.append(self.v_tilde.copy())
 

GPy/likelihoods/ep_mixed_noise.py

@@ -0,0 +1,385 @@
+# Copyright (c) 2013, Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+from scipy import stats
+from ..util.linalg import pdinv,mdot,jitchol,chol_inv,DSYR,tdot,dtrtrs
+from likelihood import likelihood
+
+class EP_Mixed_Noise(likelihood):
+    def __init__(self,data_list,noise_model_list,epsilon=1e-3,power_ep=[1.,1.]):
+        """
+        Expectation Propagation
+
+        Arguments
+        ---------
+        :param data_list: list of outputs
+        :param noise_model_list: a list of noise models
+        :param epsilon: Convergence criterion, maximum squared difference allowed between mean updates to stop iterations
+        :type epsilon: float
+        :param power_ep: list of power ep parameters
+        """
+        assert len(data_list) == len(noise_model_list)
+        self.noise_model_list = noise_model_list
+        n_list = [data.size for data in data_list]
+        self.n_models = len(data_list)
+        self.n_params = [noise_model._get_params().size for noise_model in noise_model_list]
+        self.index = np.vstack([np.repeat(i,n)[:,None] for i,n in zip(range(self.n_models),n_list)])
+        self.epsilon = epsilon
+        self.eta, self.delta = power_ep
+        self.data = np.vstack(data_list)
+        self.N, self.output_dim = self.data.shape
+        self.is_heteroscedastic = True
+        self.Nparams = 0#FIXME
+        self._transf_data = np.vstack([noise_model._preprocess_values(data) for noise_model,data in zip(noise_model_list,data_list)])
+        #TODO non-gaussian index
+
+        #Initial values - Likelihood approximation parameters:
+        #p(y|f) = t(f|tau_tilde,v_tilde)
+        self.tau_tilde = np.zeros(self.N)
+        self.v_tilde = np.zeros(self.N)
+
+        #initial values for the GP variables
+        self.Y = np.zeros((self.N,1))
+        self.covariance_matrix = np.eye(self.N)
+        self.precision = np.ones(self.N)[:,None]
+        self.Z = 0
+        self.YYT = None
+        self.V = self.precision * self.Y
+        self.VVT_factor = self.V
+        self.trYYT = 0.
+
+    def restart(self):
+        self.tau_tilde = np.zeros(self.N)
+        self.v_tilde = np.zeros(self.N)
+        self.Y = np.zeros((self.N,1))
+        self.covariance_matrix = np.eye(self.N)
+        self.precision = np.ones(self.N)[:,None]
+        self.Z = 0
+        self.YYT = None
+        self.V = self.precision * self.Y
+        self.VVT_factor = self.V
+        self.trYYT = 0.
+
+    def predictive_values(self,mu,var,full_cov,noise_model):
+        """
+        Predicts the output given the GP
+
+        :param mu: GP's mean
+        :param var: GP's variance
+        :param full_cov: whether to return the full covariance matrix, or just the diagonal
+        :type full_cov: False|True
+        :param noise_model: noise model to use
+        :type noise_model: integer
+        """
+        if full_cov:
+            raise NotImplementedError, "Cannot make correlated predictions with an EP likelihood"
+        #_mu = []
+        #_var = []
+        #_q1 = []
+        #_q2 = []
+        #for m,v,o in zip(mu,var,output.flatten()):
+        #    a,b,c,d = self.noise_model_list[int(o)].predictive_values(m,v)
+        #    _mu.append(a)
+        #    _var.append(b)
+        #    _q1.append(c)
+        #    _q2.append(d)
+        #return np.vstack(_mu),np.vstack(_var),np.vstack(_q1),np.vstack(_q2)
+        return self.noise_model_list[noise_model].predictive_values(mu,var)
+
+    def _get_params(self):
+        return np.hstack([noise_model._get_params().flatten() for noise_model in self.noise_model_list])
+
+    def _get_param_names(self):
+        names = []
+        for noise_model in self.noise_model_list:
+           names += noise_model._get_param_names()
+        return names
+
+    def _set_params(self,p):
+        cs_params = np.cumsum([0]+self.n_params)
+        for i in range(len(self.n_params)):
+            self.noise_model_list[i]._set_params(p[cs_params[i]:cs_params[i+1]])
+
+    def _gradients(self,partial):
+        #NOTE this is not tested
+        return np.hstack([noise_model._gradients(partial) for noise_model in self.noise_model_list])
+
+    def _compute_GP_variables(self):
+        #Variables to be called from GP
+        mu_tilde = self.v_tilde/self.tau_tilde #When calling EP, this variable is used instead of Y in the GP model
+        sigma_sum = 1./self.tau_ + 1./self.tau_tilde
+        mu_diff_2 = (self.v_/self.tau_ - mu_tilde)**2
+        self.Z = np.sum(np.log(self.Z_hat)) + 0.5*np.sum(np.log(sigma_sum)) + 0.5*np.sum(mu_diff_2/sigma_sum) #Normalization constant, aka Z_ep
+
+        self.Y =  mu_tilde[:,None]
+        self.YYT = np.dot(self.Y,self.Y.T)
+        self.covariance_matrix = np.diag(1./self.tau_tilde)
+        self.precision = self.tau_tilde[:,None]
+        self.V = self.precision * self.Y
+        self.VVT_factor = self.V
+        self.trYYT = np.trace(self.YYT)
+
+    def fit_full(self,K):
+        """
+        The expectation-propagation algorithm.
+        For nomenclature see Rasmussen & Williams 2006.
+        """
+        #Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma)
+        mu = np.zeros(self.N)
+        Sigma = K.copy()
+
+        """
+        Initial values - Cavity distribution parameters:
+        q_(f|mu_,sigma2_) = Product{q_i(f|mu_i,sigma2_i)}
+        sigma_ = 1./tau_
+        mu_ = v_/tau_
+        """
+        self.tau_ = np.empty(self.N,dtype=float)
+        self.v_ = np.empty(self.N,dtype=float)
+
+        #Initial values - Marginal moments
+        z = np.empty(self.N,dtype=float)
+        self.Z_hat = np.empty(self.N,dtype=float)
+        phi = np.empty(self.N,dtype=float)
+        mu_hat = np.empty(self.N,dtype=float)
+        sigma2_hat = np.empty(self.N,dtype=float)
+
+        #Approximation
+        epsilon_np1 = self.epsilon + 1.
+        epsilon_np2 = self.epsilon + 1.
+       	self.iterations = 0
+        self.np1 = [self.tau_tilde.copy()]
+        self.np2 = [self.v_tilde.copy()]
+        while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon:
+            update_order = np.random.permutation(self.N)
+            for i in update_order:
+                #Cavity distribution parameters
+                self.tau_[i] = 1./Sigma[i,i] - self.eta*self.tau_tilde[i]
+                self.v_[i] = mu[i]/Sigma[i,i] - self.eta*self.v_tilde[i]
+                #Marginal moments
+                self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model_list[self.index[i]].moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
+                #Site parameters update
+                Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma[i,i])
+                Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma[i,i])
+                self.tau_tilde[i] += Delta_tau
+                self.v_tilde[i] += Delta_v
+                #Posterior distribution parameters update
+                DSYR(Sigma,Sigma[:,i].copy(), -float(Delta_tau/(1.+ Delta_tau*Sigma[i,i])))
+                mu = np.dot(Sigma,self.v_tilde)
+                self.iterations += 1
+            #Sigma recomptutation with Cholesky decompositon
+            Sroot_tilde_K = np.sqrt(self.tau_tilde)[:,None]*K
+            B = np.eye(self.N) + np.sqrt(self.tau_tilde)[None,:]*Sroot_tilde_K
+            L = jitchol(B)
+            V,info = dtrtrs(L,Sroot_tilde_K,lower=1)
+            Sigma = K - np.dot(V.T,V)
+            mu = np.dot(Sigma,self.v_tilde)
+            epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.N
+            epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.N
+            self.np1.append(self.tau_tilde.copy())
+            self.np2.append(self.v_tilde.copy())
+
+        return self._compute_GP_variables()
+
+    def fit_DTC(self, Kmm, Kmn):
+        """
+        The expectation-propagation algorithm with sparse pseudo-input.
+        For nomenclature see ... 2013.
+        """
+        num_inducing = Kmm.shape[0]
+
+        #TODO: this doesn't work with uncertain inputs!
+
+        """
+        Prior approximation parameters:
+        q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0)
+        Sigma0 = Qnn = Knm*Kmmi*Kmn
+        """
+        KmnKnm = np.dot(Kmn,Kmn.T)
+        Lm = jitchol(Kmm)
+        Lmi = chol_inv(Lm)
+        Kmmi = np.dot(Lmi.T,Lmi)
+        KmmiKmn = np.dot(Kmmi,Kmn)
+        Qnn_diag = np.sum(Kmn*KmmiKmn,-2)
+        LLT0 = Kmm.copy()
+
+        #Kmmi, Lm, Lmi, Kmm_logdet = pdinv(Kmm)
+        #KmnKnm = np.dot(Kmn, Kmn.T)
+        #KmmiKmn = np.dot(Kmmi,Kmn)
+        #Qnn_diag = np.sum(Kmn*KmmiKmn,-2)
+        #LLT0 = Kmm.copy()
+
+        """
+        Posterior approximation: q(f|y) = N(f| mu, Sigma)
+        Sigma = Diag + P*R.T*R*P.T + K
+        mu = w + P*Gamma
+        """
+        mu = np.zeros(self.N)
+        LLT = Kmm.copy()
+        Sigma_diag = Qnn_diag.copy()
+
+        """
+        Initial values - Cavity distribution parameters:
+        q_(g|mu_,sigma2_) = Product{q_i(g|mu_i,sigma2_i)}
+        sigma_ = 1./tau_
+        mu_ = v_/tau_
+        """
+        self.tau_ = np.empty(self.N,dtype=float)
+        self.v_ = np.empty(self.N,dtype=float)
+
+        #Initial values - Marginal moments
+        z = np.empty(self.N,dtype=float)
+        self.Z_hat = np.empty(self.N,dtype=float)
+        phi = np.empty(self.N,dtype=float)
+        mu_hat = np.empty(self.N,dtype=float)
+        sigma2_hat = np.empty(self.N,dtype=float)
+
+        #Approximation
+        epsilon_np1 = 1
+        epsilon_np2 = 1
+       	self.iterations = 0
+        np1 = [self.tau_tilde.copy()]
+        np2 = [self.v_tilde.copy()]
+        while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon:
+            update_order = np.random.permutation(self.N)
+            for i in update_order:
+                #Cavity distribution parameters
+                self.tau_[i] = 1./Sigma_diag[i] - self.eta*self.tau_tilde[i]
+                self.v_[i] = mu[i]/Sigma_diag[i] - self.eta*self.v_tilde[i]
+                #Marginal moments
+                self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model_list[self.index[i]].moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
+                #Site parameters update
+                Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i])
+                Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i])
+                self.tau_tilde[i] += Delta_tau
+                self.v_tilde[i] += Delta_v
+                #Posterior distribution parameters update
+                DSYR(LLT,Kmn[:,i].copy(),Delta_tau) #LLT = LLT + np.outer(Kmn[:,i],Kmn[:,i])*Delta_tau
+                L = jitchol(LLT)
+                #cholUpdate(L,Kmn[:,i]*np.sqrt(Delta_tau))
+                V,info = dtrtrs(L,Kmn,lower=1)
+                Sigma_diag = np.sum(V*V,-2)
+                si = np.sum(V.T*V[:,i],-1)
+                mu += (Delta_v-Delta_tau*mu[i])*si
+                self.iterations += 1
+            #Sigma recomputation with Cholesky decompositon
+            LLT = LLT0 + np.dot(Kmn*self.tau_tilde[None,:],Kmn.T)
+            L = jitchol(LLT)
+            V,info = dtrtrs(L,Kmn,lower=1)
+            V2,info = dtrtrs(L.T,V,lower=0)
+            Sigma_diag = np.sum(V*V,-2)
+            Knmv_tilde = np.dot(Kmn,self.v_tilde)
+            mu = np.dot(V2.T,Knmv_tilde)
+            epsilon_np1 = sum((self.tau_tilde-np1[-1])**2)/self.N
+            epsilon_np2 = sum((self.v_tilde-np2[-1])**2)/self.N
+            np1.append(self.tau_tilde.copy())
+            np2.append(self.v_tilde.copy())
+
+        self._compute_GP_variables()
+
+    def fit_FITC(self, Kmm, Kmn, Knn_diag):
+        """
+        The expectation-propagation algorithm with sparse pseudo-input.
+        For nomenclature see Naish-Guzman and Holden, 2008.
+        """
+        num_inducing = Kmm.shape[0]
+
+        """
+        Prior approximation parameters:
+        q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0)
+        Sigma0 = diag(Knn-Qnn) + Qnn, Qnn = Knm*Kmmi*Kmn
+        """
+        Lm = jitchol(Kmm)
+        Lmi = chol_inv(Lm)
+        Kmmi = np.dot(Lmi.T,Lmi)
+        P0 = Kmn.T
+        KmnKnm = np.dot(P0.T, P0)
+        KmmiKmn = np.dot(Kmmi,P0.T)
+        Qnn_diag = np.sum(P0.T*KmmiKmn,-2)
+        Diag0 = Knn_diag - Qnn_diag
+        R0 = jitchol(Kmmi).T
+
+        """
+        Posterior approximation: q(f|y) = N(f| mu, Sigma)
+        Sigma = Diag + P*R.T*R*P.T + K
+        mu = w + P*Gamma
+        """
+        self.w = np.zeros(self.N)
+        self.Gamma = np.zeros(num_inducing)
+        mu = np.zeros(self.N)
+        P = P0.copy()
+        R = R0.copy()
+        Diag = Diag0.copy()
+        Sigma_diag = Knn_diag
+        RPT0 = np.dot(R0,P0.T)
+
+        """
+        Initial values - Cavity distribution parameters:
+        q_(g|mu_,sigma2_) = Product{q_i(g|mu_i,sigma2_i)}
+        sigma_ = 1./tau_
+        mu_ = v_/tau_
+        """
+        self.tau_ = np.empty(self.N,dtype=float)
+        self.v_ = np.empty(self.N,dtype=float)
+
+        #Initial values - Marginal moments
+        z = np.empty(self.N,dtype=float)
+        self.Z_hat = np.empty(self.N,dtype=float)
+        phi = np.empty(self.N,dtype=float)
+        mu_hat = np.empty(self.N,dtype=float)
+        sigma2_hat = np.empty(self.N,dtype=float)
+
+        #Approximation
+        epsilon_np1 = 1
+        epsilon_np2 = 1
+       	self.iterations = 0
+        self.np1 = [self.tau_tilde.copy()]
+        self.np2 = [self.v_tilde.copy()]
+        while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon:
+            update_order = np.random.permutation(self.N)
+            for i in update_order:
+                #Cavity distribution parameters
+                self.tau_[i] = 1./Sigma_diag[i] - self.eta*self.tau_tilde[i]
+                self.v_[i] = mu[i]/Sigma_diag[i] - self.eta*self.v_tilde[i]
+                #Marginal moments
+                self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model_list[self.index[i]].moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
+                #Site parameters update
+                Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i])
+                Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i])
+                self.tau_tilde[i] += Delta_tau
+                self.v_tilde[i] += Delta_v
+                #Posterior distribution parameters update
+                dtd1 = Delta_tau*Diag[i] + 1.
+                dii = Diag[i]
+                Diag[i] = dii - (Delta_tau * dii**2.)/dtd1
+                pi_ = P[i,:].reshape(1,num_inducing)
+                P[i,:] = pi_ - (Delta_tau*dii)/dtd1 * pi_
+                Rp_i = np.dot(R,pi_.T)
+                RTR = np.dot(R.T,np.dot(np.eye(num_inducing) - Delta_tau/(1.+Delta_tau*Sigma_diag[i]) * np.dot(Rp_i,Rp_i.T),R))
+                R = jitchol(RTR).T
+                self.w[i] += (Delta_v - Delta_tau*self.w[i])*dii/dtd1
+                self.Gamma += (Delta_v - Delta_tau*mu[i])*np.dot(RTR,P[i,:].T)
+                RPT = np.dot(R,P.T)
+                Sigma_diag = Diag + np.sum(RPT.T*RPT.T,-1)
+                mu = self.w + np.dot(P,self.Gamma)
+                self.iterations += 1
+            #Sigma recomptutation with Cholesky decompositon
+            Iplus_Dprod_i = 1./(1.+ Diag0 * self.tau_tilde)
+            Diag = Diag0 * Iplus_Dprod_i
+            P = Iplus_Dprod_i[:,None] * P0
+            safe_diag = np.where(Diag0 < self.tau_tilde, self.tau_tilde/(1.+Diag0*self.tau_tilde), (1. - Iplus_Dprod_i)/Diag0)
+            L = jitchol(np.eye(num_inducing) + np.dot(RPT0,safe_diag[:,None]*RPT0.T))
+            R,info = dtrtrs(L,R0,lower=1)
+            RPT = np.dot(R,P.T)
+            Sigma_diag = Diag + np.sum(RPT.T*RPT.T,-1)
+            self.w = Diag * self.v_tilde
+            self.Gamma = np.dot(R.T, np.dot(RPT,self.v_tilde))
+            mu = self.w + np.dot(P,self.Gamma)
+            epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.N
+            epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.N
+            self.np1.append(self.tau_tilde.copy())
+            self.np2.append(self.v_tilde.copy())
+
+        return self._compute_GP_variables()

GPy/likelihoods/gaussian.py

@@ -7,9 +7,9 @@ class Gaussian(likelihood):
     """
     Likelihood class for doing Expectation propagation
 
-    :param Y: observed output (Nx1 numpy.darray)
+    :param data: observed output
-    ..Note:: Y values allowed depend on the likelihood_function used
+    :type data: Nx1 numpy.darray
-    :param variance :
+    :param variance: noise parameter
     :param normalize:  whether to normalize the data before computing (predictions will be in original scales)
     :type normalize: False|True
     """
@@ -34,6 +34,8 @@ class Gaussian(likelihood):
         self._variance = np.asarray(variance) + 1.
         self._set_params(np.asarray(variance))
 
+        super(Gaussian, self).__init__()
+
     def set_data(self, data):
         self.data = data
         self.N, D = data.shape
@@ -88,11 +90,5 @@ class Gaussian(likelihood):
             _95pc = mean + 2.*np.sqrt(true_var)
         return mean, true_var, _5pc, _95pc
 
-    def fit_full(self):
-        """
-        No approximations needed
-        """
-        pass
-
     def _gradients(self, partial):
         return np.sum(partial)

GPy/likelihoods/gaussian_mixed_noise.py

@@ -0,0 +1,108 @@
+# Copyright (c) 2013, Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+from scipy import stats
+from ..util.linalg import pdinv,mdot,jitchol,chol_inv,DSYR,tdot,dtrtrs
+from likelihood import likelihood
+from . import Gaussian
+
+
+class Gaussian_Mixed_Noise(likelihood):
+    """
+    Gaussian Likelihood for multiple outputs
+
+    This is a wrapper around likelihood.Gaussian class
+
+    :param data_list: data observations
+    :type data_list: list of numpy arrays (num_data_output_i x 1), one array per output
+    :param noise_params: noise parameters of each output
+    :type noise_params: list of floats, one per output
+    :param normalize:  whether to normalize the data before computing (predictions will be in original scales)
+    :type normalize: False|True
+    """
+    def __init__(self, data_list, noise_params=None, normalize=True):
+        self.Nparams = len(data_list)
+        self.n_list = [data.size for data in data_list]
+        self.index = np.vstack([np.repeat(i,n)[:,None] for i,n in zip(range(self.Nparams),self.n_list)])
+
+        if noise_params is None:
+            noise_params = [1.] * self.Nparams
+        else:
+            assert self.Nparams == len(noise_params), 'Number of noise parameters does not match the number of noise models.'
+
+        self.noise_model_list = [Gaussian(Y,variance=v,normalize = normalize) for Y,v in zip(data_list,noise_params)]
+        self.n_params = [noise_model._get_params().size for noise_model in self.noise_model_list]
+        self.data = np.vstack(data_list)
+        self.N, self.output_dim = self.data.shape
+        self._offset = np.zeros((1, self.output_dim))
+        self._scale = np.ones((1, self.output_dim))
+
+        self.is_heteroscedastic = True
+        self.Z = 0. # a correction factor which accounts for the approximation made
+
+        self.set_data(data_list)
+        self._set_params(np.asarray(noise_params))
+
+        super(Gaussian_Mixed_Noise, self).__init__()
+
+    def set_data(self, data_list):
+        self.data = np.vstack(data_list)
+        self.N, D = self.data.shape
+        assert D == self.output_dim
+        self.Y = (self.data - self._offset) / self._scale
+        if D > self.N:
+            raise NotImplementedError
+            #self.YYT = np.dot(self.Y, self.Y.T)
+            #self.trYYT = np.trace(self.YYT)
+            #self.YYT_factor = jitchol(self.YYT)
+        else:
+            self.YYT = None
+            self.trYYT = np.sum(np.square(self.Y))
+            self.YYT_factor = self.Y
+
+    def predictive_values(self,mu,var,full_cov,noise_model):
+        """
+        Predicts the output given the GP
+
+        :param mu: GP's mean
+        :param var: GP's variance
+        :param full_cov: whether to return the full covariance matrix, or just the diagonal
+        :type full_cov: False|True
+        :param noise_model: noise model to use
+        :type noise_model: integer
+        """
+        if full_cov:
+            raise NotImplementedError, "Cannot make correlated predictions with an EP likelihood"
+        return self.noise_model_list[noise_model].predictive_values(mu,var,full_cov)
+
+    def _get_params(self):
+        return np.hstack([noise_model._get_params().flatten() for noise_model in self.noise_model_list])
+
+    def _get_param_names(self):
+        if len(self.noise_model_list) == 1:
+            names = self.noise_model_list[0]._get_param_names()
+        else:
+            names = []
+            for noise_model,i in zip(self.noise_model_list,range(len(self.n_list))):
+                names.append(''.join(noise_model._get_param_names() + ['_%s' %i]))
+        return names
+
+    def _set_params(self,p):
+        cs_params = np.cumsum([0]+self.n_params)
+
+        for i in range(len(self.n_params)):
+            self.noise_model_list[i]._set_params(p[cs_params[i]:cs_params[i+1]])
+        self.precision = np.hstack([np.repeat(noise_model.precision,n) for noise_model,n in zip(self.noise_model_list,self.n_list)])[:,None]
+
+        self.V = self.precision * self.Y
+        self.VVT_factor = self.precision * self.YYT_factor
+        self.covariance_matrix = np.eye(self.N) * 1./self.precision
+
+    def _gradients(self,partial):
+        gradients = []
+        aux = np.cumsum([0]+self.n_list)
+        for ai,af,noise_model in zip(aux[:-1],aux[1:],self.noise_model_list):
+            gradients += [noise_model._gradients(partial[ai:af])]
+        return np.hstack(gradients)

GPy/likelihoods/laplace.py

@@ -13,7 +13,7 @@ from functools import partial
 class Laplace(likelihood):
     """Laplace approximation to a posterior"""
 
-    def __init__(self, data, likelihood_function, extra_data=None, opt='rasm'):
+    def __init__(self, data, noise_model, extra_data=None, opt='rasm'):
         """
         Laplace Approximation
 
@@ -28,13 +28,13 @@ class Laplace(likelihood):
         ---------
 
         :data: array of data the likelihood function is approximating
-        :likelihood_function: likelihood function - subclass of likelihood_function
+        :noise_model: likelihood function - subclass of noise_model
         :extra_data: additional data used by some likelihood functions, for example survival likelihoods need censoring data
         :opt: Optimiser to use, rasm numerically stable, ncg or nelder-mead (latter only work with 1d data)
 
         """
         self.data = data
-        self.likelihood_function = likelihood_function
+        self.noise_model = noise_model
         self.extra_data = extra_data
         self.opt = opt
 
@@ -45,6 +45,7 @@ class Laplace(likelihood):
         self.NORMAL_CONST = ((0.5 * self.N) * np.log(2 * np.pi))
 
         self.restart()
+        likelihood.__init__(self)
 
     def restart(self):
         #Initial values for the GP variables
@@ -59,49 +60,55 @@ class Laplace(likelihood):
     def predictive_values(self, mu, var, full_cov):
         if full_cov:
             raise NotImplementedError("Cannot make correlated predictions with an Laplace likelihood")
-        return self.likelihood_function.predictive_values(mu, var)
+        return self.noise_model.predictive_values(mu, var)
 
     def _get_params(self):
-        return np.asarray(self.likelihood_function._get_params())
+        return np.asarray(self.noise_model._get_params())
 
     def _get_param_names(self):
-        return self.likelihood_function._get_param_names()
+        return self.noise_model._get_param_names()
 
     def _set_params(self, p):
-        return self.likelihood_function._set_params(p)
+        return self.noise_model._set_params(p)
 
     def _shared_gradients_components(self):
-        d3lik_d3fhat = self.likelihood_function.d3lik_d3f(self.data, self.f_hat, extra_data=self.extra_data)
+        d3lik_d3fhat = self.noise_model.d3lik_d3f(self.data, self.f_hat, extra_data=self.extra_data)
         dL_dfhat = 0.5*(np.diag(self.Ki_W_i)[:, None]*d3lik_d3fhat).T #why isn't this -0.5?
         I_KW_i = np.eye(self.N) - np.dot(self.K, self.Wi_K_i)
         return dL_dfhat, I_KW_i
 
-    def _Kgradients(self, dK_dthetaK, X):
+    def _Kgradients(self):
         """
         Gradients with respect to prior kernel parameters
         """
         dL_dfhat, I_KW_i = self._shared_gradients_components()
-        dlp = self.likelihood_function.dlik_df(self.data, self.f_hat)
+        dlp = self.noise_model.dlik_df(self.data, self.f_hat)
 
         #Explicit
-        expl_a = np.dot(self.Ki_f, self.Ki_f.T)
+        #expl_a = np.dot(self.Ki_f, self.Ki_f.T)
-        expl_b = self.Wi_K_i
+        #expl_b = self.Wi_K_i
-        expl = 0.5*expl_a - 0.5*expl_b
+        #expl = 0.5*expl_a - 0.5*expl_b
-        dL_dthetaK_exp = dK_dthetaK(expl, X)
+        #dL_dthetaK_exp = dK_dthetaK(expl, X)
 
         #Implicit
         impl = mdot(dlp, dL_dfhat, I_KW_i)
-        dL_dthetaK_imp = dK_dthetaK(impl, X)
+
-        #print "K: dL_dthetaK_exp: {}     dL_dthetaK_implicit: {}".format(dL_dthetaK_exp, dL_dthetaK_imp)
+        #No longer required as we are computing these in the gp already otherwise we would take them away and add them back
-        dL_dthetaK = dL_dthetaK_exp + dL_dthetaK_imp
+        #dL_dthetaK_imp = dK_dthetaK(impl, X)
-        return dL_dthetaK
+        #dL_dthetaK = dL_dthetaK_exp + dL_dthetaK_imp
+        #dL_dK = expl + impl
+
+        #No need to compute explicit as we are computing dZ_dK to account for the difference
+        #Between the K gradients of a normal GP, and the K gradients including the implicit part
+        dL_dK = impl
+        return dL_dK
 
     def _gradients(self, partial):
         """
         Gradients with respect to likelihood parameters
         """
         dL_dfhat, I_KW_i = self._shared_gradients_components()
-        dlik_dthetaL, dlik_grad_dthetaL, dlik_hess_dthetaL = self.likelihood_function._gradients(self.data, self.f_hat)
+        dlik_dthetaL, dlik_grad_dthetaL, dlik_hess_dthetaL = self.noise_model._laplace_gradients(self.data, self.f_hat)
 
         num_params = len(dlik_dthetaL)
         # make space for one derivative for each likelihood parameter
@@ -163,12 +170,13 @@ class Laplace(likelihood):
         Y_tilde = Wi*self.Ki_f + self.f_hat
 
         #self.Wi_K_i = self.W_12*self.Bi*self.W_12.T #same as rasms R
-        self.Wi_K_i = self.W_12*cho_solve((self.B_chol, True), np.diagflat(self.W_12))
+        #self.Wi_K_i = self.W_12*cho_solve((self.B_chol, True), np.diagflat(self.W_12))
+        self.Wi_K_i = self.W12BiW12
         #self.Wi_K_i, _, _, self.ln_det_Wi_K = pdinv(self.Sigma_tilde + self.K) # TODO: Check if Wi_K_i == R above and same with det below
 
         self.ln_det_Wi_K = pddet(self.Sigma_tilde + self.K)
 
-        self.lik = self.likelihood_function.link_function(self.data, self.f_hat, extra_data=self.extra_data)
+        self.lik = self.noise_model.link_function(self.data, self.f_hat, extra_data=self.extra_data)
 
         self.y_Wi_Ki_i_y = mdot(Y_tilde.T, self.Wi_K_i, Y_tilde)
         Z_tilde = (+ self.lik
@@ -185,6 +193,10 @@ class Laplace(likelihood):
         self.covariance_matrix = self.Sigma_tilde
         self.precision = 1.0 / np.diag(self.covariance_matrix)[:, None]
 
+        #Compute dZ_dK which is how the approximated distributions gradients differ from the dL_dK computed for other likelihoods
+        self.dZ_dK = self._Kgradients()
+        #+ 0.5*self.Wi_K_i - 0.5*np.dot(self.Ki_f, self.Ki_f.T) #since we are not adding the K gradients explicit part theres no need to compute this again
+
     def fit_full(self, K):
         """
         The laplace approximation algorithm, find K and expand hessian
@@ -205,27 +217,19 @@ class Laplace(likelihood):
 
     def _compute_likelihood_variables(self):
         #At this point get the hessian matrix (or vector as W is diagonal)
-        self.W = -self.likelihood_function.d2lik_d2f(self.data, self.f_hat, extra_data=self.extra_data)
+        self.W = -self.noise_model.d2lik_d2f(self.data, self.f_hat, extra_data=self.extra_data)
-
-        if not self.likelihood_function.log_concave:
-            #print "Under 1e-6: {}".format(np.sum(self.W < 1e-6))
-            self.W[self.W < 1e-6] = 1e-6  # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur
-                                       #If the likelihood is non-log-concave. We wan't to say that there is a negative variance
-                                       #To cause the posterior to become less certain than the prior and likelihood,
-                                       #This is a property only held by non-log-concave likelihoods
 
         #TODO: Could save on computation when using rasm by returning these, means it isn't just a "mode finder" though
-        self.B, self.B_chol, self.W_12 = self._compute_B_statistics(self.K, self.W)
+        self.W12BiW12, self.ln_B_det = self._compute_B_statistics(self.K, self.W, np.eye(self.N))
-        self.Bi, _, _, self.ln_B_det = pdinv(self.B)
 
         #Do the computation again at f to get Ki_f which is useful
-        #b = self.W*self.f_hat + self.likelihood_function.dlik_df(self.data, self.f_hat, extra_data=self.extra_data)
+        #b = self.W*self.f_hat + self.noise_model.dlik_df(self.data, self.f_hat, extra_data=self.extra_data)
         #solve_chol = cho_solve((self.B_chol, True), np.dot(self.W_12*self.K, b))
         #a = b - self.W_12*solve_chol
         self.Ki_f = self.a
 
         self.f_Ki_f = np.dot(self.f_hat.T, self.Ki_f)
-        self.Ki_W_i = self.K - mdot(self.K, self.W_12*cho_solve((self.B_chol, True), np.diagflat(self.W_12)), self.K)
+        self.Ki_W_i = self.K - mdot(self.K, self.W12BiW12, self.K)
 
         #For det, |I + KW| == |I + W_12*K*W_12|
         #self.ln_I_KW_det = pddet(np.eye(self.N) + self.W_12*self.K*self.W_12.T)
@@ -233,12 +237,12 @@ class Laplace(likelihood):
         #self.ln_I_KW_det = pddet(np.eye(self.N) + np.dot(self.K, self.W))
         #self.ln_z_hat = (- 0.5*self.f_Ki_f
                          #- self.ln_I_KW_det
-                         #+ self.likelihood_function.link_function(self.data, self.f_hat, extra_data=self.extra_data)
+                         #+ self.noise_model.link_function(self.data, self.f_hat, extra_data=self.extra_data)
                          #)
 
         return self._compute_GP_variables()
 
-    def _compute_B_statistics(self, K, W):
+    def _compute_B_statistics(self, K, W, a):
         """Rasmussen suggests the use of a numerically stable positive definite matrix B
         Which has a positive diagonal element and can be easyily inverted
 
@@ -246,17 +250,28 @@ class Laplace(likelihood):
         :W: Negative hessian at a point (diagonal matrix)
         :returns: (B, L)
         """
+        if not self.noise_model.log_concave:
+            #print "Under 1e-10: {}".format(np.sum(W < 1e-10))
+            W[W < 1e-6] = 1e-6  # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur
+                                # If the likelihood is non-log-concave. We wan't to say that there is a negative variance
+                                # To cause the posterior to become less certain than the prior and likelihood,
+                                # This is a property only held by non-log-concave likelihoods
+
+
         #W is diagonal so its sqrt is just the sqrt of the diagonal elements
         W_12 = np.sqrt(W)
         B = np.eye(self.N) + W_12*K*W_12.T
         L = jitchol(B)
-        return (B, L, W_12)
+
+        W12BiW12= W_12*cho_solve((L, True), W_12*a)
+        ln_B_det = 2*np.sum(np.log(np.diag(L)))
+        return (W12BiW12, ln_B_det)
 
     def nelder_mode(self, K):
         f = np.zeros((self.N, 1))
         self.Ki, _, _, self.ln_K_det = pdinv(K)
         def obj(f):
-            res = -1 * (self.likelihood_function.link_function(self.data[:, 0], f, extra_data=self.extra_data) - 0.5*np.dot(f.T, np.dot(self.Ki, f)))
+            res = -1 * (self.noise_model.link_function(self.data[:, 0], f, extra_data=self.extra_data) - 0.5*np.dot(f.T, np.dot(self.Ki, f)))
             return float(res)
 
         res = sp.optimize.minimize(obj, f, method='nelder-mead', options={'xtol': 1e-7, 'maxiter': 25000, 'disp': True})
@@ -276,16 +291,16 @@ class Laplace(likelihood):
         #FIXME: Can we get rid of this horrible reshaping?
         #ONLY WORKS FOR 1D DATA
         def obj(f):
-            res = -1 * (self.likelihood_function.link_function(self.data[:, 0], f, extra_data=self.extra_data) - 0.5 * np.dot(f.T, np.dot(self.Ki, f))
+            res = -1 * (self.noise_model.link_function(self.data[:, 0], f, extra_data=self.extra_data) - 0.5 * np.dot(f.T, np.dot(self.Ki, f))
                         - self.NORMAL_CONST)
             return float(res)
 
         def obj_grad(f):
-            res = -1 * (self.likelihood_function.dlik_df(self.data[:, 0], f, extra_data=self.extra_data) - np.dot(self.Ki, f))
+            res = -1 * (self.noise_model.dlik_df(self.data[:, 0], f, extra_data=self.extra_data) - np.dot(self.Ki, f))
             return np.squeeze(res)
 
         def obj_hess(f):
-            res = -1 * (np.diag(self.likelihood_function.d2lik_d2f(self.data[:, 0], f, extra_data=self.extra_data)) - self.Ki)
+            res = -1 * (np.diag(self.noise_model.d2lik_d2f(self.data[:, 0], f, extra_data=self.extra_data)) - self.Ki)
             return np.squeeze(res)
 
         f_hat = sp.optimize.fmin_ncg(obj, f, fprime=obj_grad, fhess=obj_hess, disp=False)
@@ -301,7 +316,7 @@ class Laplace(likelihood):
         :MAX_RESTART: Maximum number of restarts (reducing step_size) before forcing finish of optimisation
         :returns: f_mode
         """
-        #self.old_before_s = self.likelihood_function._get_params()
+        #self.old_before_s = self.noise_model._get_params()
         #print "before: ", self.old_before_s
         #if self.old_before_s < 1e-5:
 
@@ -317,7 +332,7 @@ class Laplace(likelihood):
         old_obj = np.inf
 
         def obj(a, f):
-            return -0.5*np.dot(a.T, f) + self.likelihood_function.link_function(self.data, f, extra_data=self.extra_data)
+            return -0.5*np.dot(a.T, f) + self.noise_model.link_function(self.data, f, extra_data=self.extra_data)
 
         difference = np.inf
         epsilon = 1e-6
@@ -326,23 +341,17 @@ class Laplace(likelihood):
         i = 0
 
         while difference > epsilon and i < MAX_ITER:# and rs < MAX_RESTART:
-            W = -self.likelihood_function.d2lik_d2f(self.data, f, extra_data=self.extra_data)
+            W = -self.noise_model.d2lik_d2f(self.data, f, extra_data=self.extra_data)
-            #W = np.maximum(W, 0)
-            if not self.likelihood_function.log_concave:
-                #print "Under 1e-10: {}".format(np.sum(W < 1e-10))
-                W[W < 1e-6] = 1e-6     # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur
-                                    # If the likelihood is non-log-concave. We wan't to say that there is a negative variance
-                                    # To cause the posterior to become less certain than the prior and likelihood,
-                                    # This is a property only held by non-log-concave likelihoods
-            B, L, W_12 = self._compute_B_statistics(K, W.copy())
 
             W_f = W*f
-            grad = self.likelihood_function.dlik_df(self.data, f, extra_data=self.extra_data)
+            grad = self.noise_model.dlik_df(self.data, f, extra_data=self.extra_data)
 
             b = W_f + grad
-            solve_L = cho_solve((L, True), W_12*np.dot(K, b))
+            #TODO!!!
+            W12BiW12Kb, _ = self._compute_B_statistics(K, W.copy(), np.dot(K, b))
+            #solve_L = cho_solve((L, True), W_12*np.dot(K, b))
             #Work out the DIRECTION that we want to move in, but don't choose the stepsize yet
-            full_step_a = b - W_12*solve_L
+            full_step_a = b - W12BiW12Kb
             da = full_step_a - old_a
 
             f_old = f.copy()
@@ -355,7 +364,7 @@ class Laplace(likelihood):
 
             i_o = partial(inner_obj, old_a=old_a, da=da, K=K)
             #new_obj = sp.optimize.brent(i_o, tol=1e-4, maxiter=20)
-            new_obj = sp.optimize.minimize_scalar(i_o, method='brent', tol=1e-4, options={'maxiter':20}).fun
+            new_obj = sp.optimize.minimize_scalar(i_o, method='brent', tol=1e-4, options={'maxiter':30}).fun
             f = self.f.copy()
             a = self.a.copy()
 
@@ -435,13 +444,13 @@ class Laplace(likelihood):
                     pb.close('all')
 
         #FIXME: DELETE THESE
-        self.old_W = W.copy()
+        #self.old_W = W.copy()
-        self.old_grad = grad.copy()
+        #self.old_grad = grad.copy()
-        self.old_B = B.copy()
+        #self.old_B = B.copy()
-        self.old_W_12 = W_12.copy()
+        #self.old_W_12 = W_12.copy()
-        self.old_ff = f.copy()
+        #self.old_ff = f.copy()
-        self.old_K = self.K.copy()
+        #self.old_K = self.K.copy()
-        self.old_s = self.likelihood_function._get_params()
+        #self.old_s = self.noise_model._get_params()
         #print "after: ", self.old_s
         #print "FINAL a max: {} a min: {} a var: {}".format(np.max(self.a), np.min(self.a), np.var(self.a))
         self.a = a

GPy/likelihoods/likelihood.py

@@ -1,7 +1,8 @@
 import numpy as np
 import copy
+from ..core.parameterized import Parameterized
 
-class likelihood:
+class likelihood(Parameterized):
     """
     The atom for a likelihood class
 
@@ -9,17 +10,20 @@ class likelihood:
     (Gaussian) inherits directly from this, as does the EP algorithm
 
     Some things must be defined for this to work properly:
-    self.Y : the effective Gaussian target of the GP
+
-    self.N, self.D : Y.shape
+        - self.Y : the effective Gaussian target of the GP
-    self.covariance_matrix : the effective (noise) covariance of the GP targets
+        - self.N, self.D : Y.shape
-    self.Z : a factor which gets added to the likelihood (0 for a Gaussian, Z_EP for EP)
+        - self.covariance_matrix : the effective (noise) covariance of the GP targets
-    self.is_heteroscedastic : enables significant computational savings in GP
+        - self.Z : a factor which gets added to the likelihood (0 for a Gaussian, Z_EP for EP)
-    self.precision : a scalar or vector representation of the effective target precision
+        - self.is_heteroscedastic : enables significant computational savings in GP
-    self.YYT : (optional) = np.dot(self.Y, self.Y.T) enables computational savings for D>N
+        - self.precision : a scalar or vector representation of the effective target precision
-    self.V : self.precision * self.Y 
+        - self.YYT : (optional) = np.dot(self.Y, self.Y.T) enables computational savings for D>N
+        - self.V : self.precision * self.Y
+
     """
-    def __init__(self,data):
+    def __init__(self):
-        raise ValueError, "this class is not to be instantiated"
+        Parameterized.__init__(self)
+        self.dZ_dK = 0
 
     def _get_params(self):
         raise NotImplementedError
@@ -33,12 +37,20 @@ class likelihood:
     def fit(self):
         raise NotImplementedError
 
+    def fit_full(self, K):
+        """
+        No approximations needed by default
+        """
+        pass
+
+    def restart(self):
+        """
+        No need to restart if not an approximation
+        """
+        pass
+
     def _gradients(self, partial):
         raise NotImplementedError
 
     def predictive_values(self, mu, var):
         raise NotImplementedError
-
-    def copy(self):
-        """ Returns a (deep) copy of the current likelihood """
-        return copy.deepcopy(self)

GPy/likelihoods/link_functions.py

@@ -1,46 +0,0 @@
-# Copyright (c) 2012, 2013 Ricardo Andrade
-# Licensed under the BSD 3-clause license (see LICENSE.txt)
-
-
-import numpy as np
-from scipy import stats
-import scipy as sp
-import pylab as pb
-from ..util.plot import gpplot
-from ..util.univariate_Gaussian import std_norm_pdf,std_norm_cdf
-
-class LinkFunction(object):
-    """
-    Link function class for doing non-Gaussian likelihoods approximation
-
-    :param Y: observed output (Nx1 numpy.darray)
-    ..Note:: Y values allowed depend on the likelihood_function used
-    """
-    def __init__(self):
-        pass
-
-class Probit(LinkFunction):
-    """
-    Probit link function: Squashes a likelihood between 0 and 1
-    """
-    def transf(self,mu):
-        pass
-
-    def inv_transf(self,f):
-        pass
-
-    def log_inv_transf(self,f):
-        pass
-
-class Nothing(LinkFunction):
-    """
-    Probit link function: Squashes a likelihood between 0 and 1
-    """
-    def transf(self,mu):
-        return mu
-
-    def inv_transf(self,f):
-        return f
-
-    def log_inv_transf(self,f):
-        return np.log(f)

GPy/likelihoods/noise_model_constructors.py

@@ -0,0 +1,115 @@
+# Copyright (c) 2013, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+import noise_models
+
+def binomial(gp_link=None):
+    """
+    Construct a binomial likelihood
+
+    :param gp_link: a GPy gp_link function
+    """
+    if gp_link is None:
+        gp_link = noise_models.gp_transformations.Probit()
+    #else:
+    #    assert isinstance(gp_link,noise_models.gp_transformations.GPTransformation), 'gp_link function is not valid.'
+
+    if isinstance(gp_link,noise_models.gp_transformations.Probit):
+        analytical_mean = True
+        analytical_variance = False
+
+    elif isinstance(gp_link,noise_models.gp_transformations.Heaviside):
+        analytical_mean = True
+        analytical_variance = True
+
+    else:
+        analytical_mean = False
+        analytical_variance = False
+
+    return noise_models.binomial_noise.Binomial(gp_link,analytical_mean,analytical_variance)
+
+def exponential(gp_link=None):
+    """
+    Construct a binomial likelihood
+
+    :param gp_link: a GPy gp_link function
+    """
+    if gp_link is None:
+        gp_link = noise_models.gp_transformations.Identity()
+
+    analytical_mean = False
+    analytical_variance = False
+    return noise_models.exponential_noise.Exponential(gp_link,analytical_mean,analytical_variance)
+
+def gaussian_ep(gp_link=None,variance=1.):
+    """
+    Construct a gaussian likelihood
+
+    :param gp_link: a GPy gp_link function
+    :param variance: scalar
+    """
+    if gp_link is None:
+        gp_link = noise_models.gp_transformations.Identity()
+    #else:
+    #    assert isinstance(gp_link,noise_models.gp_transformations.GPTransformation), 'gp_link function is not valid.'
+
+    analytical_mean = False
+    analytical_variance = False
+    return noise_models.gaussian_noise.Gaussian(gp_link,analytical_mean,analytical_variance,variance)
+
+def poisson(gp_link=None):
+    """
+    Construct a Poisson likelihood
+
+    :param gp_link: a GPy gp_link function
+    """
+    if gp_link is None:
+        gp_link = noise_models.gp_transformations.Log_ex_1()
+    #else:
+    #    assert isinstance(gp_link,noise_models.gp_transformations.GPTransformation), 'gp_link function is not valid.'
+    analytical_mean = False
+    analytical_variance = False
+    return noise_models.poisson_noise.Poisson(gp_link,analytical_mean,analytical_variance)
+
+def gamma(gp_link=None,beta=1.):
+    """
+    Construct a Gamma likelihood
+
+    :param gp_link: a GPy gp_link function
+    :param beta: scalar
+    """
+    if gp_link is None:
+        gp_link = noise_models.gp_transformations.Log_ex_1()
+    analytical_mean = False
+    analytical_variance = False
+    return noise_models.gamma_noise.Gamma(gp_link,analytical_mean,analytical_variance,beta)
+
+def gaussian(gp_link=None, variance=2, D=None, N=None):
+    """
+    Construct a Gaussian likelihood
+
+    :param gp_link: a GPy gp_link function
+    :param variance: scalar, variance
+    """
+    if gp_link is None:
+        gp_link = noise_models.gp_transformations.Identity()
+    analytical_mean = True
+    analytical_variance = True # ?
+    return noise_models.gaussian_noise.Gaussian(gp_link, analytical_mean,
+            analytical_variance, variance=variance, D=D, N=N)
+
+def student_t(gp_link=None, deg_free=5, sigma2=2):
+    """
+    Construct a Student t likelihood
+
+    :param gp_link: a GPy gp_link function
+    :param deg_free: scalar, degrees of freedom
+    :param sigma2: scalar, variance
+    """
+    if gp_link is None:
+        gp_link = noise_models.gp_transformations.Identity()
+    analytical_mean = True
+    analytical_variance = True
+    return noise_models.student_t_noise.StudentT(gp_link, analytical_mean,
+            analytical_variance,deg_free, sigma2)

GPy/likelihoods/noise_models/__init__.py

@@ -0,0 +1,8 @@
+import noise_distributions
+import binomial_noise
+import exponential_noise
+import gaussian_noise
+import gamma_noise
+import poisson_noise
+import student_t_noise
+import gp_transformations

GPy/likelihoods/noise_models/binomial_noise.py

@@ -0,0 +1,119 @@
+# Copyright (c) 2012, 2013 Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+from scipy import stats,special
+import scipy as sp
+from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf
+import gp_transformations
+from noise_distributions import NoiseDistribution
+
+class Binomial(NoiseDistribution):
+    """
+    Probit likelihood
+    Y is expected to take values in {-1,1}
+    -----
+    $$
+    L(x) = \\Phi (Y_i*f_i)
+    $$
+    """
+    def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False):
+        super(Binomial, self).__init__(gp_link,analytical_mean,analytical_variance)
+
+    def _preprocess_values(self,Y):
+        """
+        Check if the values of the observations correspond to the values
+        assumed by the likelihood function.
+
+        ..Note:: Binary classification algorithm works better with classes {-1,1}
+        """
+        Y_prep = Y.copy()
+        Y1 = Y[Y.flatten()==1].size
+        Y2 = Y[Y.flatten()==0].size
+        assert Y1 + Y2 == Y.size, 'Binomial likelihood is meant to be used only with outputs in {0,1}.'
+        Y_prep[Y.flatten() == 0] = -1
+        return Y_prep
+
+    def _moments_match_analytical(self,data_i,tau_i,v_i):
+        """
+        Moments match of the marginal approximation in EP algorithm
+
+        :param i: number of observation (int)
+        :param tau_i: precision of the cavity distribution (float)
+        :param v_i: mean/variance of the cavity distribution (float)
+        """
+        if isinstance(self.gp_link,gp_transformations.Probit):
+            z = data_i*v_i/np.sqrt(tau_i**2 + tau_i)
+            Z_hat = std_norm_cdf(z)
+            phi = std_norm_pdf(z)
+            mu_hat = v_i/tau_i + data_i*phi/(Z_hat*np.sqrt(tau_i**2 + tau_i))
+            sigma2_hat = 1./tau_i - (phi/((tau_i**2+tau_i)*Z_hat))*(z+phi/Z_hat)
+
+        elif isinstance(self.gp_link,gp_transformations.Heaviside):
+            a = data_i*v_i/np.sqrt(tau_i)
+            Z_hat = std_norm_cdf(a)
+            N = std_norm_pdf(a)
+            mu_hat = v_i/tau_i + data_i*N/Z_hat/np.sqrt(tau_i)
+            sigma2_hat = (1. - a*N/Z_hat - np.square(N/Z_hat))/tau_i
+            if np.any(np.isnan([Z_hat, mu_hat, sigma2_hat])):
+                stop
+
+        return Z_hat, mu_hat, sigma2_hat
+
+    def _predictive_mean_analytical(self,mu,sigma):
+        if isinstance(self.gp_link,gp_transformations.Probit):
+            return stats.norm.cdf(mu/np.sqrt(1+sigma**2))
+        elif isinstance(self.gp_link,gp_transformations.Heaviside):
+            return stats.norm.cdf(mu/sigma)
+        else:
+            raise NotImplementedError
+
+    def _predictive_variance_analytical(self,mu,sigma, pred_mean):
+        if isinstance(self.gp_link,gp_transformations.Heaviside):
+            return 0.
+        else:
+            raise NotImplementedError
+
+    def _mass(self,gp,obs):
+        #NOTE obs must be in {0,1}
+        p = self.gp_link.transf(gp)
+        return p**obs * (1.-p)**(1.-obs)
+
+    def _nlog_mass(self,gp,obs):
+        p = self.gp_link.transf(gp)
+        return obs*np.log(p) + (1.-obs)*np.log(1-p)
+
+    def _dnlog_mass_dgp(self,gp,obs):
+        p = self.gp_link.transf(gp)
+        dp = self.gp_link.dtransf_df(gp)
+        return obs/p * dp - (1.-obs)/(1.-p) * dp
+
+    def _d2nlog_mass_dgp2(self,gp,obs):
+        p = self.gp_link.transf(gp)
+        return (obs/p + (1.-obs)/(1.-p))*self.gp_link.d2transf_df2(gp) + ((1.-obs)/(1.-p)**2-obs/p**2)*self.gp_link.dtransf_df(gp)
+
+    def _mean(self,gp):
+        """
+        Mass (or density) function
+        """
+        return self.gp_link.transf(gp)
+
+    def _dmean_dgp(self,gp):
+        return self.gp_link.dtransf_df(gp)
+
+    def _d2mean_dgp2(self,gp):
+        return self.gp_link.d2transf_df2(gp)
+
+    def _variance(self,gp):
+        """
+        Mass (or density) function
+        """
+        p = self.gp_link.transf(gp)
+        return p*(1.-p)
+
+    def _dvariance_dgp(self,gp):
+        return self.gp_link.dtransf_df(gp)*(1. - 2.*self.gp_link.transf(gp))
+
+    def _d2variance_dgp2(self,gp):
+        return self.gp_link.d2transf_df2(gp)*(1. - 2.*self.gp_link.transf(gp)) - 2*self.gp_link.dtransf_df(gp)**2

GPy/likelihoods/noise_models/exponential_noise.py

@@ -0,0 +1,68 @@
+# Copyright (c) 2012, 2013 Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+from scipy import stats,special
+import scipy as sp
+from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf
+import gp_transformations
+from noise_distributions import NoiseDistribution
+
+class Exponential(NoiseDistribution):
+    """
+    Expoential likelihood
+    Y is expected to take values in {0,1,2,...}
+    -----
+    $$
+    L(x) = \exp(\lambda) * \lambda**Y_i / Y_i!
+    $$
+    """
+    def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False):
+        super(Exponential, self).__init__(gp_link,analytical_mean,analytical_variance)
+
+    def _preprocess_values(self,Y):
+        return Y
+
+    def _mass(self,gp,obs):
+        """
+        Mass (or density) function
+        """
+        return np.exp(-obs/self.gp_link.transf(gp))/self.gp_link.transf(gp)
+
+    def _nlog_mass(self,gp,obs):
+        """
+        Negative logarithm of the un-normalized distribution: factors that are not a function of gp are omitted
+        """
+        return obs/self.gp_link.transf(gp) + np.log(self.gp_link.transf(gp))
+
+    def _dnlog_mass_dgp(self,gp,obs):
+        return ( 1./self.gp_link.transf(gp) - obs/self.gp_link.transf(gp)**2) * self.gp_link.dtransf_df(gp)
+
+    def _d2nlog_mass_dgp2(self,gp,obs):
+        fgp = self.gp_link.transf(gp)
+        return (2*obs/fgp**3 - 1./fgp**2) * self.gp_link.dtransf_df(gp)**2 + ( 1./fgp - obs/fgp**2) * self.gp_link.d2transf_df2(gp)
+
+    def _mean(self,gp):
+        """
+        Mass (or density) function
+        """
+        return self.gp_link.transf(gp)
+
+    def _dmean_dgp(self,gp):
+        return self.gp_link.dtransf_df(gp)
+
+    def _d2mean_dgp2(self,gp):
+        return self.gp_link.d2transf_df2(gp)
+
+    def _variance(self,gp):
+        """
+        Mass (or density) function
+        """
+        return self.gp_link.transf(gp)**2
+
+    def _dvariance_dgp(self,gp):
+        return 2*self.gp_link.transf(gp)*self.gp_link.dtransf_df(gp)
+
+    def _d2variance_dgp2(self,gp):
+        return 2 * (self.gp_link.dtransf_df(gp)**2 + self.gp_link.transf(gp)*self.gp_link.d2transf_df2(gp))

GPy/likelihoods/noise_models/gamma_noise.py

@@ -0,0 +1,71 @@
+# Copyright (c) 2012, 2013 Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+from scipy import stats,special
+import scipy as sp
+from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf
+import gp_transformations
+from noise_distributions import NoiseDistribution
+
+class Gamma(NoiseDistribution):
+    """
+    Gamma likelihood
+    Y is expected to take values in {0,1,2,...}
+    -----
+    $$
+    L(x) = \exp(\lambda) * \lambda**Y_i / Y_i!
+    $$
+    """
+    def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False,beta=1.):
+        self.beta = beta
+        super(Gamma, self).__init__(gp_link,analytical_mean,analytical_variance)
+
+    def _preprocess_values(self,Y):
+        return Y
+
+    def _mass(self,gp,obs):
+        """
+        Mass (or density) function
+        """
+        #return stats.gamma.pdf(obs,a = self.gp_link.transf(gp)/self.variance,scale=self.variance)
+        alpha = self.gp_link.transf(gp)*self.beta
+        return obs**(alpha - 1.) * np.exp(-self.beta*obs) * self.beta**alpha / special.gamma(alpha)
+
+    def _nlog_mass(self,gp,obs):
+        """
+        Negative logarithm of the un-normalized distribution: factors that are not a function of gp are omitted
+        """
+        alpha = self.gp_link.transf(gp)*self.beta
+        return (1. - alpha)*np.log(obs) + self.beta*obs - alpha * np.log(self.beta) + np.log(special.gamma(alpha))
+
+    def _dnlog_mass_dgp(self,gp,obs):
+        return -self.gp_link.dtransf_df(gp)*self.beta*np.log(obs) + special.psi(self.gp_link.transf(gp)*self.beta) * self.gp_link.dtransf_df(gp)*self.beta
+
+    def _d2nlog_mass_dgp2(self,gp,obs):
+        return -self.gp_link.d2transf_df2(gp)*self.beta*np.log(obs) + special.polygamma(1,self.gp_link.transf(gp)*self.beta)*(self.gp_link.dtransf_df(gp)*self.beta)**2 + special.psi(self.gp_link.transf(gp)*self.beta)*self.gp_link.d2transf_df2(gp)*self.beta
+
+    def _mean(self,gp):
+        """
+        Mass (or density) function
+        """
+        return self.gp_link.transf(gp)
+
+    def _dmean_dgp(self,gp):
+        return self.gp_link.dtransf_df(gp)
+
+    def _d2mean_dgp2(self,gp):
+        return self.gp_link.d2transf_df2(gp)
+
+    def _variance(self,gp):
+        """
+        Mass (or density) function
+        """
+        return self.gp_link.transf(gp)/self.beta
+
+    def _dvariance_dgp(self,gp):
+        return self.gp_link.dtransf_df(gp)/self.beta
+
+    def _d2variance_dgp2(self,gp):
+        return self.gp_link.d2transf_df2(gp)/self.beta

GPy/likelihoods/noise_models/gaussian_noise.py

@@ -0,0 +1,208 @@
+# Copyright (c) 2012, 2013 Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+from scipy import stats,special
+import scipy as sp
+from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf
+import gp_transformations
+from noise_distributions import NoiseDistribution
+
+class Gaussian(NoiseDistribution):
+    """
+    Gaussian likelihood
+
+    :param mean: mean value of the Gaussian distribution
+    :param variance: mean value of the Gaussian distribution
+    """
+    def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False,variance=1., D=None, N=None):
+        self.variance = variance
+        self.D = D
+        self.N = N
+        self._set_params(np.asarray(variance))
+        super(Gaussian, self).__init__(gp_link,analytical_mean,analytical_variance)
+
+    def _get_params(self):
+        return np.array([self.variance])
+
+    def _get_param_names(self):
+        return ['noise_model_variance']
+
+    def _set_params(self, p):
+        self.variance = float(p)
+        self.I = np.eye(self.N)
+        self.covariance_matrix = self.I * self.variance
+        self.Ki = self.I*(1.0 / self.variance)
+        self.ln_det_K = np.sum(np.log(np.diag(self.covariance_matrix)))
+
+    def _laplace_gradients(self, y, f, extra_data=None):
+        #must be listed in same order as 'get_param_names'
+        derivs = ([self.dlik_dvar(y, f, extra_data=extra_data)],
+                  [self.dlik_df_dvar(y, f, extra_data=extra_data)],
+                  [self.d2lik_d2f_dvar(y, f, extra_data=extra_data)]
+                 ) # lists as we might learn many parameters
+        # ensure we have gradients for every parameter we want to optimize
+        assert len(derivs[0]) == len(self._get_param_names())
+        assert len(derivs[1]) == len(self._get_param_names())
+        assert len(derivs[2]) == len(self._get_param_names())
+        return derivs
+
+    def _gradients(self,partial):
+        return np.zeros(1)
+        #return np.sum(partial)
+
+    def _preprocess_values(self,Y):
+        """
+        Check if the values of the observations correspond to the values
+        assumed by the likelihood function.
+        """
+        return Y
+
+    def _moments_match_analytical(self,data_i,tau_i,v_i):
+        """
+        Moments match of the marginal approximation in EP algorithm
+
+        :param i: number of observation (int)
+        :param tau_i: precision of the cavity distribution (float)
+        :param v_i: mean/variance of the cavity distribution (float)
+        """
+        sigma2_hat = 1./(1./self.variance + tau_i)
+        mu_hat = sigma2_hat*(data_i/self.variance + v_i)
+        sum_var = self.variance + 1./tau_i
+        Z_hat = 1./np.sqrt(2.*np.pi*sum_var)*np.exp(-.5*(data_i - v_i/tau_i)**2./sum_var)
+        return Z_hat, mu_hat, sigma2_hat
+
+    def _predictive_mean_analytical(self,mu,sigma):
+        new_sigma2 = self.predictive_variance(mu,sigma)
+        return new_sigma2*(mu/sigma**2 + self.gp_link.transf(mu)/self.variance)
+
+    def _predictive_variance_analytical(self,mu,sigma):
+        return 1./(1./self.variance + 1./sigma**2)
+
+    def _mass(self,gp,obs):
+        #return std_norm_pdf( (self.gp_link.transf(gp)-obs)/np.sqrt(self.variance) )
+        return stats.norm.pdf(obs,self.gp_link.transf(gp),np.sqrt(self.variance))
+
+    def _nlog_mass(self,gp,obs):
+        return .5*((self.gp_link.transf(gp)-obs)**2/self.variance + np.log(2.*np.pi*self.variance))
+
+    def _dnlog_mass_dgp(self,gp,obs):
+        return (self.gp_link.transf(gp)-obs)/self.variance * self.gp_link.dtransf_df(gp)
+
+    def _d2nlog_mass_dgp2(self,gp,obs):
+        return ((self.gp_link.transf(gp)-obs)*self.gp_link.d2transf_df2(gp) + self.gp_link.dtransf_df(gp)**2)/self.variance
+
+    def _mean(self,gp):
+        """
+        Mass (or density) function
+        """
+        return self.gp_link.transf(gp)
+
+    def _dmean_dgp(self,gp):
+        return self.gp_link.dtransf_df(gp)
+
+    def _d2mean_dgp2(self,gp):
+        return self.gp_link.d2transf_df2(gp)
+
+    def _variance(self,gp):
+        """
+        Mass (or density) function
+        """
+        return self.variance
+
+    def _dvariance_dgp(self,gp):
+        return 0
+
+    def _d2variance_dgp2(self,gp):
+        return 0
+
+    def link_function(self, y, f, extra_data=None):
+        """link_function $\ln p(y|f)$
+        $$\ln p(y_{i}|f_{i}) = \ln $$
+
+        :y: data
+        :f: latent variables f
+        :extra_data: extra_data which is not used in student t distribution
+        :returns: float(likelihood evaluated for this point)
+
+        """
+        assert y.shape == f.shape
+        e = y - f
+        eeT = np.dot(e, e.T)
+        objective = (- 0.5*self.D*np.log(2*np.pi)
+                     - 0.5*self.ln_det_K
+                     - (0.5/self.variance)*np.dot(e.T, e) # As long as K is diagonal
+                     )
+        return np.sum(objective)
+
+    def dlik_df(self, y, f, extra_data=None):
+        """
+        Gradient of the link function at y, given f w.r.t f
+
+        :y: data
+        :f: latent variables f
+        :extra_data: extra_data which is not used in student t distribution
+        :returns: gradient of likelihood evaluated at points
+
+        """
+        assert y.shape == f.shape
+        s2_i = (1.0/self.variance)*self.I
+        grad = np.dot(s2_i, y) - np.dot(s2_i, f)
+        return grad
+
+    def d2lik_d2f(self, y, f, extra_data=None):
+        """
+        Hessian at this point (if we are only looking at the link function not the prior) the hessian will be 0 unless i == j
+        i.e. second derivative link_function at y given f f_j  w.r.t f and f_j
+
+        Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
+        (the distribution for y_{i} depends only on f_{i} not on f_{j!=i}
+
+        :y: data
+        :f: latent variables f
+        :extra_data: extra_data which is not used in student t distribution
+        :returns: array which is diagonal of covariance matrix (second derivative of likelihood evaluated at points)
+        """
+        assert y.shape == f.shape
+        s2_i = (1.0/self.variance)*self.I
+        hess = np.diag(-s2_i)[:, None] # FIXME: CAREFUL THIS MAY NOT WORK WITH MULTIDIMENSIONS?
+        return hess
+
+    def d3lik_d3f(self, y, f, extra_data=None):
+        """
+        Third order derivative link_function (log-likelihood ) at y given f f_j w.r.t f and f_j
+
+        $$\frac{d^{3}p(y_{i}|f_{i})}{d^{3}f} = \frac{-2(v+1)((y_{i} - f_{i})^3 - 3(y_{i} - f_{i}) \sigma^{2} v))}{((y_{i} - f_{i}) + \sigma^{2} v)^3}$$
+        """
+        assert y.shape == f.shape
+        d3lik_d3f = np.diagonal(0*self.I)[:, None] # FIXME: CAREFUL THIS MAY NOT WORK WITH MULTIDIMENSIONS?
+        return d3lik_d3f
+
+    def dlik_dvar(self, y, f, extra_data=None):
+        """
+        Gradient of the likelihood (lik) w.r.t sigma parameter (standard deviation)
+        """
+        assert y.shape == f.shape
+        e = y - f
+        s_4 = 1.0/(self.variance**2)
+        dlik_dsigma = -0.5*self.N/self.variance + 0.5*s_4*np.dot(e.T, e)
+        return np.sum(dlik_dsigma) # Sure about this sum?
+
+    def dlik_df_dvar(self, y, f, extra_data=None):
+        """
+        Gradient of the dlik_df w.r.t sigma parameter (standard deviation)
+        """
+        assert y.shape == f.shape
+        s_4 = 1.0/(self.variance**2)
+        dlik_grad_dsigma = -np.dot(s_4*self.I, y) + np.dot(s_4*self.I, f)
+        return dlik_grad_dsigma
+
+    def d2lik_d2f_dvar(self, y, f, extra_data=None):
+        """
+        Gradient of the hessian (d2lik_d2f) w.r.t sigma parameter (standard deviation)
+
+        $$\frac{d}{d\sigma}(\frac{d^{2}p(y_{i}|f_{i})}{d^{2}f}) = \frac{2\sigma v(v + 1)(\sigma^2 v - 3(y-f)^2)}{((y-f)^2 + \sigma^2 v)^3}$$
+        """
+        assert y.shape == f.shape
+        dlik_hess_dsigma = np.diag((1.0/(self.variance**2))*self.I)[:, None]
+        return dlik_hess_dsigma

GPy/likelihoods/noise_models/gp_transformations.py

@@ -0,0 +1,133 @@
+# Copyright (c) 2012, 2013 Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+from scipy import stats
+import scipy as sp
+import pylab as pb
+from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf,inv_std_norm_cdf
+
+class GPTransformation(object):
+    """
+    Link function class for doing non-Gaussian likelihoods approximation
+
+    :param Y: observed output (Nx1 numpy.darray)
+
+    .. note:: Y values allowed depend on the likelihood_function used
+
+    """
+    def __init__(self):
+        pass
+
+    def transf(self,f):
+        """
+        Gaussian process tranformation function, latent space -> output space
+        """
+        pass
+
+    def dtransf_df(self,f):
+        """
+        derivative of transf(f) w.r.t. f
+        """
+        pass
+
+    def d2transf_df2(self,f):
+        """
+        second derivative of transf(f) w.r.t. f
+        """
+        pass
+
+class Identity(GPTransformation):
+    """
+    .. math::
+
+        g(f) = f
+
+    """
+    def transf(self,f):
+        return f
+
+    def dtransf_df(self,f):
+        return 1.
+
+    def d2transf_df2(self,f):
+        return 0
+
+
+class Probit(GPTransformation):
+    """
+    .. math::
+
+        g(f) = \\Phi^{-1} (mu)
+
+    """
+    def transf(self,f):
+        return std_norm_cdf(f)
+
+    def dtransf_df(self,f):
+        return std_norm_pdf(f)
+
+    def d2transf_df2(self,f):
+        return -f * std_norm_pdf(f)
+
+class Log(GPTransformation):
+    """
+    .. math::
+
+        g(f) = \\log(\\mu)
+
+    """
+    def transf(self,f):
+        return np.exp(f)
+
+    def dtransf_df(self,f):
+        return np.exp(f)
+
+    def d2transf_df2(self,f):
+        return np.exp(f)
+
+class Log_ex_1(GPTransformation):
+    """
+    .. math::
+
+        g(f) = \\log(\\exp(\\mu) - 1)
+
+    """
+    def transf(self,f):
+        return np.log(1.+np.exp(f))
+
+    def dtransf_df(self,f):
+        return np.exp(f)/(1.+np.exp(f))
+
+    def d2transf_df2(self,f):
+        aux = np.exp(f)/(1.+np.exp(f))
+        return aux*(1.-aux)
+
+class Reciprocal(GPTransformation):
+    def transf(sefl,f):
+        return 1./f
+
+    def dtransf_df(self,f):
+        return -1./f**2
+
+    def d2transf_df2(self,f):
+        return 2./f**3
+
+class Heaviside(GPTransformation):
+    """
+
+    .. math::
+
+        g(f) = I_{x \\in A}
+
+    """
+    def transf(self,f):
+        #transformation goes here
+        return np.where(f>0, 1, 0)
+
+    def dtransf_df(self,f):
+        raise NotImplementedError, "This function is not differentiable!"
+
+    def d2transf_df2(self,f):
+        raise NotImplementedError, "This function is not differentiable!"

GPy/likelihoods/noise_models/noise_distributions.py

@@ -0,0 +1,417 @@
+# Copyright (c) 2012, 2013 Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+from scipy import stats,special
+import scipy as sp
+import pylab as pb
+from GPy.util.plot import gpplot
+from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf
+import gp_transformations
+
+
+class NoiseDistribution(object):
+    """
+    Likelihood class for doing Expectation propagation
+
+    :param Y: observed output (Nx1 numpy.darray)
+
+    .. note:: Y values allowed depend on the LikelihoodFunction used
+    """
+    def __init__(self,gp_link,analytical_mean=False,analytical_variance=False):
+        assert isinstance(gp_link,gp_transformations.GPTransformation), "gp_link is not a valid GPTransformation."
+        self.gp_link = gp_link
+        self.analytical_mean = analytical_mean
+        self.analytical_variance = analytical_variance
+        if self.analytical_mean:
+            self.moments_match = self._moments_match_analytical
+            self.predictive_mean = self._predictive_mean_analytical
+        else:
+            self.moments_match = self._moments_match_numerical
+            self.predictive_mean = self._predictive_mean_numerical
+        if self.analytical_variance:
+            self.predictive_variance = self._predictive_variance_analytical
+        else:
+            self.predictive_variance = self._predictive_variance_numerical
+
+        self.log_concave = True
+
+    def _get_params(self):
+        return np.zeros(0)
+
+    def _get_param_names(self):
+        return []
+
+    def _set_params(self,p):
+        pass
+
+    def _gradients(self,partial):
+        return np.zeros(0)
+
+    def _preprocess_values(self,Y):
+        """
+        In case it is needed, this function assess the output values or makes any pertinent transformation on them.
+
+        :param Y: observed output
+        :type Y: Nx1 numpy.darray
+
+        """
+        return Y
+
+    def _product(self,gp,obs,mu,sigma):
+        """
+        Product between the cavity distribution and a likelihood factor.
+
+        :param gp: latent variable
+        :param obs: observed output
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        return stats.norm.pdf(gp,loc=mu,scale=sigma) * self._mass(gp,obs)
+
+    def _nlog_product_scaled(self,gp,obs,mu,sigma):
+        """
+        Negative log-product between the cavity distribution and a likelihood factor.
+
+        .. note:: The constant term in the Gaussian distribution is ignored.
+
+        :param gp: latent variable
+        :param obs: observed output
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        return .5*((gp-mu)/sigma)**2 + self._nlog_mass(gp,obs)
+
+    def _dnlog_product_dgp(self,gp,obs,mu,sigma):
+        """
+        Derivative wrt latent variable of the log-product between the cavity distribution and a likelihood factor.
+
+        :param gp: latent variable
+        :param obs: observed output
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        return (gp - mu)/sigma**2 + self._dnlog_mass_dgp(gp,obs)
+
+    def _d2nlog_product_dgp2(self,gp,obs,mu,sigma):
+        """
+        Second derivative wrt latent variable of the log-product between the cavity distribution and a likelihood factor.
+
+        :param gp: latent variable
+        :param obs: observed output
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        return 1./sigma**2 + self._d2nlog_mass_dgp2(gp,obs)
+
+    def _product_mode(self,obs,mu,sigma):
+        """
+        Newton's CG method to find the mode in _product (cavity x likelihood factor).
+
+        :param obs: observed output
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        return sp.optimize.fmin_ncg(self._nlog_product_scaled,x0=mu,fprime=self._dnlog_product_dgp,fhess=self._d2nlog_product_dgp2,args=(obs,mu,sigma),disp=False)
+
+    def _moments_match_analytical(self,obs,tau,v):
+        """
+        If available, this function computes the moments analytically.
+        """
+        pass
+
+    def _moments_match_numerical(self,obs,tau,v):
+        """
+        Lapace approximation to calculate the moments.
+
+        :param obs: observed output
+        :param tau: cavity distribution 1st natural parameter (precision)
+        :param v: cavity distribution 2nd natural paramenter (mu*precision)
+
+        """
+        mu = v/tau
+        mu_hat = self._product_mode(obs,mu,np.sqrt(1./tau))
+        sigma2_hat = 1./(tau + self._d2nlog_mass_dgp2(mu_hat,obs))
+        Z_hat = np.exp(-.5*tau*(mu_hat-mu)**2) * self._mass(mu_hat,obs)*np.sqrt(tau*sigma2_hat)
+        return Z_hat,mu_hat,sigma2_hat
+
+    def _nlog_conditional_mean_scaled(self,gp,mu,sigma):
+        """
+        Negative logarithm of the l.v.'s predictive distribution times the output's mean given the l.v.
+
+        :param gp: latent variable
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        .. note:: This function helps computing E(Y_star) = E(E(Y_star|f_star))
+
+        """
+        return .5*((gp - mu)/sigma)**2 - np.log(self._mean(gp))
+
+    def _dnlog_conditional_mean_dgp(self,gp,mu,sigma):
+        """
+        Derivative of _nlog_conditional_mean_scaled wrt. l.v.
+
+        :param gp: latent variable
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        return (gp - mu)/sigma**2 - self._dmean_dgp(gp)/self._mean(gp)
+
+    def _d2nlog_conditional_mean_dgp2(self,gp,mu,sigma):
+        """
+        Second derivative of _nlog_conditional_mean_scaled wrt. l.v.
+
+        :param gp: latent variable
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        return 1./sigma**2 - self._d2mean_dgp2(gp)/self._mean(gp) + (self._dmean_dgp(gp)/self._mean(gp))**2
+
+    def _nlog_exp_conditional_variance_scaled(self,gp,mu,sigma):
+        """
+        Negative logarithm of the l.v.'s predictive distribution times the output's variance given the l.v.
+
+        :param gp: latent variable
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        .. note:: This function helps computing E(V(Y_star|f_star))
+
+        """
+        return .5*((gp - mu)/sigma)**2 - np.log(self._variance(gp))
+
+    def _dnlog_exp_conditional_variance_dgp(self,gp,mu,sigma):
+        """
+        Derivative of _nlog_exp_conditional_variance_scaled wrt. l.v.
+
+        :param gp: latent variable
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        return (gp - mu)/sigma**2 - self._dvariance_dgp(gp)/self._variance(gp)
+
+    def _d2nlog_exp_conditional_variance_dgp2(self,gp,mu,sigma):
+        """
+        Second derivative of _nlog_exp_conditional_variance_scaled wrt. l.v.
+
+        :param gp: latent variable
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        return 1./sigma**2 - self._d2variance_dgp2(gp)/self._variance(gp) + (self._dvariance_dgp(gp)/self._variance(gp))**2
+
+    def _nlog_exp_conditional_mean_sq_scaled(self,gp,mu,sigma):
+        """
+        Negative logarithm of the l.v.'s predictive distribution times the output's mean squared given the l.v.
+
+        :param gp: latent variable
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        .. note:: This function helps computing E( E(Y_star|f_star)**2 )
+
+        """
+        return .5*((gp - mu)/sigma)**2 - 2*np.log(self._mean(gp))
+
+    def _dnlog_exp_conditional_mean_sq_dgp(self,gp,mu,sigma):
+        """
+        Derivative of _nlog_exp_conditional_mean_sq_scaled wrt. l.v.
+
+        :param gp: latent variable
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        return (gp - mu)/sigma**2 - 2*self._dmean_dgp(gp)/self._mean(gp)
+
+    def _d2nlog_exp_conditional_mean_sq_dgp2(self,gp,mu,sigma):
+        """
+        Second derivative of _nlog_exp_conditional_mean_sq_scaled wrt. l.v.
+
+        :param gp: latent variable
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        return 1./sigma**2 - 2*( self._d2mean_dgp2(gp)/self._mean(gp) - (self._dmean_dgp(gp)/self._mean(gp))**2 )
+
+    def _predictive_mean_analytical(self,mu,sigma):
+        """
+        If available, this function computes the predictive mean analytically.
+        """
+        pass
+
+    def _predictive_variance_analytical(self,mu,sigma):
+        """
+        If available, this function computes the predictive variance analytically.
+        """
+        pass
+
+    def _predictive_mean_numerical(self,mu,sigma):
+        """
+        Laplace approximation to the predictive mean: E(Y_star) = E( E(Y_star|f_star) )
+
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        maximum = sp.optimize.fmin_ncg(self._nlog_conditional_mean_scaled,x0=self._mean(mu),fprime=self._dnlog_conditional_mean_dgp,fhess=self._d2nlog_conditional_mean_dgp2,args=(mu,sigma),disp=False)
+        mean = np.exp(-self._nlog_conditional_mean_scaled(maximum,mu,sigma))/(np.sqrt(self._d2nlog_conditional_mean_dgp2(maximum,mu,sigma))*sigma)
+        """
+
+        pb.figure()
+        x = np.array([mu + step*sigma for step in np.linspace(-7,7,100)])
+        f = np.array([np.exp(-self._nlog_conditional_mean_scaled(xi,mu,sigma))/np.sqrt(2*np.pi*sigma**2) for xi in x])
+        pb.plot(x,f,'b-')
+        sigma2 = 1./self._d2nlog_conditional_mean_dgp2(maximum,mu,sigma)
+        f2 = np.exp(-.5*(x-maximum)**2/sigma2)/np.sqrt(2*np.pi*sigma2)
+        k = np.exp(-self._nlog_conditional_mean_scaled(maximum,mu,sigma))*np.sqrt(sigma2)/np.sqrt(sigma**2)
+        pb.plot(x,f2*mean,'r-')
+        pb.vlines(maximum,0,f.max())
+        """
+        return mean
+
+    def _predictive_mean_sq(self,mu,sigma):
+        """
+        Laplace approximation to the predictive mean squared: E(Y_star**2) = E( E(Y_star|f_star)**2 )
+
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+
+        """
+        maximum = sp.optimize.fmin_ncg(self._nlog_exp_conditional_mean_sq_scaled,x0=self._mean(mu),fprime=self._dnlog_exp_conditional_mean_sq_dgp,fhess=self._d2nlog_exp_conditional_mean_sq_dgp2,args=(mu,sigma),disp=False)
+        mean_squared = np.exp(-self._nlog_exp_conditional_mean_sq_scaled(maximum,mu,sigma))/(np.sqrt(self._d2nlog_exp_conditional_mean_sq_dgp2(maximum,mu,sigma))*sigma)
+        return mean_squared
+
+    def _predictive_variance_numerical(self,mu,sigma,predictive_mean=None):
+        """
+        Laplace approximation to the predictive variance: V(Y_star) = E( V(Y_star|f_star) ) + V( E(Y_star|f_star) )
+
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+        :predictive_mean: output's predictive mean, if None _predictive_mean function will be called.
+
+        """
+        # E( V(Y_star|f_star) )
+        maximum = sp.optimize.fmin_ncg(self._nlog_exp_conditional_variance_scaled,x0=self._variance(mu),fprime=self._dnlog_exp_conditional_variance_dgp,fhess=self._d2nlog_exp_conditional_variance_dgp2,args=(mu,sigma),disp=False)
+        exp_var = np.exp(-self._nlog_exp_conditional_variance_scaled(maximum,mu,sigma))/(np.sqrt(self._d2nlog_exp_conditional_variance_dgp2(maximum,mu,sigma))*sigma)
+
+        """
+        pb.figure()
+        x = np.array([mu + step*sigma for step in np.linspace(-7,7,100)])
+        f = np.array([np.exp(-self._nlog_exp_conditional_variance_scaled(xi,mu,sigma))/np.sqrt(2*np.pi*sigma**2) for xi in x])
+        pb.plot(x,f,'b-')
+        sigma2 = 1./self._d2nlog_exp_conditional_variance_dgp2(maximum,mu,sigma)
+        f2 = np.exp(-.5*(x-maximum)**2/sigma2)/np.sqrt(2*np.pi*sigma2)
+        k = np.exp(-self._nlog_exp_conditional_variance_scaled(maximum,mu,sigma))*np.sqrt(sigma2)/np.sqrt(sigma**2)
+        pb.plot(x,f2*exp_var,'r--')
+        pb.vlines(maximum,0,f.max())
+        """
+
+        #V( E(Y_star|f_star) ) =  E( E(Y_star|f_star)**2 ) - E( E(Y_star|f_star)**2 )
+        exp_exp2 = self._predictive_mean_sq(mu,sigma)
+        if predictive_mean is None:
+            predictive_mean = self.predictive_mean(mu,sigma)
+        var_exp = exp_exp2 - predictive_mean**2
+        return exp_var + var_exp
+
+    def _predictive_percentiles(self,p,mu,sigma):
+        """
+        Percentiles of the predictive distribution
+
+        :parm p: lower tail probability
+        :param mu: cavity distribution mean
+        :param sigma: cavity distribution standard deviation
+        :predictive_mean: output's predictive mean, if None _predictive_mean function will be called.
+
+        """
+        qf = stats.norm.ppf(p,mu,sigma)
+        return self.gp_link.transf(qf)
+
+    def _nlog_joint_predictive_scaled(self,x,mu,sigma):
+        """
+        Negative logarithm of the joint predictive distribution (latent variable and output).
+
+        :param x: tuple (latent variable,output)
+        :param mu: latent variable's predictive mean
+        :param sigma: latent variable's predictive standard deviation
+
+        """
+        return self._nlog_product_scaled(x[0],x[1],mu,sigma)
+
+    def _gradient_nlog_joint_predictive(self,x,mu,sigma):
+        """
+        Gradient of _nlog_joint_predictive_scaled.
+
+        :param x: tuple (latent variable,output)
+        :param mu: latent variable's predictive mean
+        :param sigma: latent variable's predictive standard deviation
+
+        .. note: Only available when the output is continuous
+
+        """
+        assert not self.discrete, "Gradient not available for discrete outputs."
+        return np.array((self._dnlog_product_dgp(gp=x[0],obs=x[1],mu=mu,sigma=sigma),self._dnlog_mass_dobs(obs=x[1],gp=x[0])))
+
+    def _hessian_nlog_joint_predictive(self,x,mu,sigma):
+        """
+        Hessian of _nlog_joint_predictive_scaled.
+
+        :param x: tuple (latent variable,output)
+        :param mu: latent variable's predictive mean
+        :param sigma: latent variable's predictive standard deviation
+
+        .. note: Only available when the output is continuous
+
+        """
+        assert not self.discrete, "Hessian not available for discrete outputs."
+        cross_derivative = self._d2nlog_mass_dcross(gp=x[0],obs=x[1])
+        return np.array((self._d2nlog_product_dgp2(gp=x[0],obs=x[1],mu=mu,sigma=sigma),cross_derivative,cross_derivative,self._d2nlog_mass_dobs2(obs=x[1],gp=x[0]))).reshape(2,2)
+
+    def _joint_predictive_mode(self,mu,sigma):
+        """
+        Negative logarithm of the joint predictive distribution (latent variable and output).
+
+        :param x: tuple (latent variable,output)
+        :param mu: latent variable's predictive mean
+        :param sigma: latent variable's predictive standard deviation
+
+        """
+        return sp.optimize.fmin_ncg(self._nlog_joint_predictive_scaled,x0=(mu,self.gp_link.transf(mu)),fprime=self._gradient_nlog_joint_predictive,fhess=self._hessian_nlog_joint_predictive,args=(mu,sigma),disp=False)
+
+    def predictive_values(self,mu,var):
+        """
+        Compute  mean, variance and conficence interval (percentiles 5 and 95) of the  prediction.
+
+        :param mu: mean of the latent variable
+        :param var: variance of the latent variable
+
+        """
+        if isinstance(mu,float) or isinstance(mu,int):
+            mu = [mu]
+            var = [var]
+        pred_mean = []
+        pred_var = []
+        q1 = []
+        q3 = []
+        for m,s in zip(mu,np.sqrt(var)):
+            pred_mean.append(self.predictive_mean(m,s))
+            pred_var.append(self.predictive_variance(m,s,pred_mean[-1]))
+            q1.append(self._predictive_percentiles(.025,m,s))
+            q3.append(self._predictive_percentiles(.975,m,s))
+        pred_mean = np.vstack(pred_mean)
+        pred_var = np.vstack(pred_var)
+        q1 = np.vstack(q1)
+        q3 = np.vstack(q3)
+        return pred_mean, pred_var, q1, q3

GPy/likelihoods/noise_models/poisson_noise.py

@@ -0,0 +1,69 @@
+# Copyright (c) 2012, 2013 Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+from scipy import stats,special
+import scipy as sp
+from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf
+import gp_transformations
+from noise_distributions import NoiseDistribution
+
+class Poisson(NoiseDistribution):
+    """
+    Poisson likelihood
+
+    .. math::
+        L(x) = \\exp(\\lambda) * \\frac{\\lambda^Y_i}{Y_i!}
+
+    ..Note: Y is expected to take values in {0,1,2,...}
+    """
+    def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False):
+        super(Poisson, self).__init__(gp_link,analytical_mean,analytical_variance)
+
+    def _preprocess_values(self,Y): #TODO
+        return Y
+
+    def _mass(self,gp,obs):
+        """
+        Mass (or density) function
+        """
+        return stats.poisson.pmf(obs,self.gp_link.transf(gp))
+
+    def _nlog_mass(self,gp,obs):
+        """
+        Negative logarithm of the un-normalized distribution: factors that are not a function of gp are omitted
+        """
+        return self.gp_link.transf(gp) - obs * np.log(self.gp_link.transf(gp)) + np.log(special.gamma(obs+1))
+
+    def _dnlog_mass_dgp(self,gp,obs):
+        return self.gp_link.dtransf_df(gp) * (1. - obs/self.gp_link.transf(gp))
+
+    def _d2nlog_mass_dgp2(self,gp,obs):
+        d2_df = self.gp_link.d2transf_df2(gp)
+        transf = self.gp_link.transf(gp)
+        return obs * ((self.gp_link.dtransf_df(gp)/transf)**2 - d2_df/transf) + d2_df
+
+    def _mean(self,gp):
+        """
+        Mass (or density) function
+        """
+        return self.gp_link.transf(gp)
+
+    def _dmean_dgp(self,gp):
+        return self.gp_link.dtransf_df(gp)
+
+    def _d2mean_dgp2(self,gp):
+        return self.gp_link.d2transf_df2(gp)
+
+    def _variance(self,gp):
+        """
+        Mass (or density) function
+        """
+        return self.gp_link.transf(gp)
+
+    def _dvariance_dgp(self,gp):
+        return self.gp_link.dtransf_df(gp)
+
+    def _d2variance_dgp2(self,gp):
+        return self.gp_link.d2transf_df2(gp)

GPy/likelihoods/noise_models/student_t_noise.py

@@ -0,0 +1,249 @@
+# Copyright (c) 2012, 2013 Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+from scipy import stats,special
+import scipy as sp
+import gp_transformations
+from noise_distributions import NoiseDistribution
+from scipy import stats, integrate
+from scipy.special import gammaln, gamma
+
+class StudentT(NoiseDistribution):
+    """
+    Student T likelihood
+
+    For nomanclature see Bayesian Data Analysis 2003 p576
+
+    $$\ln p(y_{i}|f_{i}) = \ln \Gamma(\frac{v+1}{2}) - \ln \Gamma(\frac{v}{2})\sqrt{v \pi}\sigma - \frac{v+1}{2}\ln (1 + \frac{1}{v}\left(\frac{y_{i} - f_{i}}{\sigma}\right)^2)$$
+
+    .. math::
+        Fill in maths
+
+    """
+    def __init__(self,gp_link=None,analytical_mean=True,analytical_variance=True, deg_free=5, sigma2=2):
+        self.v = deg_free
+        self.sigma2 = sigma2
+
+        self._set_params(np.asarray(sigma2))
+        super(StudentT, self).__init__(gp_link,analytical_mean,analytical_variance)
+        self.log_concave = False
+
+    def _get_params(self):
+        return np.asarray(self.sigma2)
+
+    def _get_param_names(self):
+        return ["t_noise_std2"]
+
+    def _set_params(self, x):
+        self.sigma2 = float(x)
+
+    @property
+    def variance(self, extra_data=None):
+        return (self.v / float(self.v - 2)) * self.sigma2
+
+    def link_function(self, y, f, extra_data=None):
+        """link_function $\ln p(y|f)$
+        $$\ln p(y_{i}|f_{i}) = \ln \Gamma(\frac{v+1}{2}) - \ln \Gamma(\frac{v}{2})\sqrt{v \pi}\sigma - \frac{v+1}{2}\ln (1 + \frac{1}{v}\left(\frac{y_{i} - f_{i}}{\sigma}\right)^2$$
+
+        For wolfram alpha import parts for derivative of sigma are -log(sqrt(v*pi)*s) -(1/2)*(v + 1)*log(1 + (1/v)*((y-f)/(s))^2))
+
+        :y: data
+        :f: latent variables f
+        :extra_data: extra_data which is not used in student t distribution
+        :returns: float(likelihood evaluated for this point)
+
+        """
+        assert y.shape == f.shape
+        e = y - f
+        objective = (+ gammaln((self.v + 1) * 0.5)
+                     - gammaln(self.v * 0.5)
+                     - 0.5*np.log(self.sigma2 * self.v * np.pi)
+                     - 0.5*(self.v + 1)*np.log(1 + (1/np.float(self.v))*((e**2)/self.sigma2))
+                    )
+        return np.sum(objective)
+
+    def dlik_df(self, y, f, extra_data=None):
+        """
+        Gradient of the link function at y, given f w.r.t f
+
+        $$\frac{dp(y_{i}|f_{i})}{df} = \frac{(v+1)(y_{i}-f_{i})}{(y_{i}-f_{i})^{2} + \sigma^{2}v}$$
+
+        :y: data
+        :f: latent variables f
+        :extra_data: extra_data which is not used in student t distribution
+        :returns: gradient of likelihood evaluated at points
+
+        """
+        assert y.shape == f.shape
+        e = y - f
+        grad = ((self.v + 1) * e) / (self.v * self.sigma2 + (e**2))
+        return grad
+
+    def d2lik_d2f(self, y, f, extra_data=None):
+        """
+        Hessian at this point (if we are only looking at the link function not the prior) the hessian will be 0 unless i == j
+        i.e. second derivative link_function at y given f f_j  w.r.t f and f_j
+
+        Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
+        (the distribution for y_{i} depends only on f_{i} not on f_{j!=i}
+
+        $$\frac{d^{2}p(y_{i}|f_{i})}{d^{3}f} = \frac{(v+1)((y_{i}-f_{i})^{2} - \sigma^{2}v)}{((y_{i}-f_{i})^{2} + \sigma^{2}v)^{2}}$$
+
+        :y: data
+        :f: latent variables f
+        :extra_data: extra_data which is not used in student t distribution
+        :returns: array which is diagonal of covariance matrix (second derivative of likelihood evaluated at points)
+        """
+        assert y.shape == f.shape
+        e = y - f
+        hess = ((self.v + 1)*(e**2 - self.v*self.sigma2)) / ((self.sigma2*self.v + e**2)**2)
+        return hess
+
+    def d3lik_d3f(self, y, f, extra_data=None):
+        """
+        Third order derivative link_function (log-likelihood ) at y given f f_j w.r.t f and f_j
+
+        $$\frac{d^{3}p(y_{i}|f_{i})}{d^{3}f} = \frac{-2(v+1)((y_{i} - f_{i})^3 - 3(y_{i} - f_{i}) \sigma^{2} v))}{((y_{i} - f_{i}) + \sigma^{2} v)^3}$$
+        """
+        assert y.shape == f.shape
+        e = y - f
+        d3lik_d3f = ( -(2*(self.v + 1)*(-e)*(e**2 - 3*self.v*self.sigma2)) /
+                       ((e**2 + self.sigma2*self.v)**3)
+                    )
+        return d3lik_d3f
+
+    def dlik_dvar(self, y, f, extra_data=None):
+        """
+        Gradient of the likelihood (lik) w.r.t sigma parameter (standard deviation)
+
+        Terms relavent to derivatives wrt sigma are:
+        -log(sqrt(v*pi)*s) -(1/2)*(v + 1)*log(1 + (1/v)*((y-f)/(s))^2))
+
+        $$\frac{dp(y_{i}|f_{i})}{d\sigma} = -\frac{1}{\sigma} + \frac{(1+v)(y_{i}-f_{i})^2}{\sigma^3 v(1 + \frac{1}{v}(\frac{(y_{i} - f_{i})}{\sigma^2})^2)}$$
+        """
+        assert y.shape == f.shape
+        e = y - f
+        dlik_dvar = self.v*(e**2 - self.sigma2)/(2*self.sigma2*(self.sigma2*self.v + e**2))
+        return np.sum(dlik_dvar) #May not want to sum over all dimensions if using many D?
+
+    def dlik_df_dvar(self, y, f, extra_data=None):
+        """
+        Gradient of the dlik_df w.r.t sigma parameter (standard deviation)
+
+        $$\frac{d}{d\sigma}(\frac{dp(y_{i}|f_{i})}{df}) = \frac{-2\sigma v(v + 1)(y_{i}-f_{i})}{(y_{i}-f_{i})^2 + \sigma^2 v)^2}$$
+        """
+        assert y.shape == f.shape
+        e = y - f
+        dlik_grad_dvar = (self.v*(self.v+1)*(-e))/((self.sigma2*self.v + e**2)**2)
+        return dlik_grad_dvar
+
+    def d2lik_d2f_dvar(self, y, f, extra_data=None):
+        """
+        Gradient of the hessian (d2lik_d2f) w.r.t sigma parameter (standard deviation)
+
+        $$\frac{d}{d\sigma}(\frac{d^{2}p(y_{i}|f_{i})}{d^{2}f}) = \frac{2\sigma v(v + 1)(\sigma^2 v - 3(y-f)^2)}{((y-f)^2 + \sigma^2 v)^3}$$
+        """
+        assert y.shape == f.shape
+        e = y - f
+        dlik_hess_dvar = ( (self.v*(self.v+1)*(self.sigma2*self.v - 3*(e**2)))
+                              / ((self.sigma2*self.v + (e**2))**3)
+                           )
+        return dlik_hess_dvar
+
+    def _laplace_gradients(self, y, f, extra_data=None):
+        #must be listed in same order as 'get_param_names'
+        derivs = ([self.dlik_dvar(y, f, extra_data=extra_data)],
+                  [self.dlik_df_dvar(y, f, extra_data=extra_data)],
+                  [self.d2lik_d2f_dvar(y, f, extra_data=extra_data)]
+                 ) # lists as we might learn many parameters
+        # ensure we have gradients for every parameter we want to optimize
+        assert len(derivs[0]) == len(self._get_param_names())
+        assert len(derivs[1]) == len(self._get_param_names())
+        assert len(derivs[2]) == len(self._get_param_names())
+        return derivs
+
+    def _predictive_variance_analytical(self, mu, sigma, predictive_mean=None):
+        """
+        Compute  mean, and conficence interval (percentiles 5 and 95) of the prediction
+
+        Need to find what the variance is at the latent points for a student t*normal p(y*|f*)p(f*)
+        (((g((v+1)/2))/(g(v/2)*s*sqrt(v*pi)))*(1+(1/v)*((y-f)/s)^2)^(-(v+1)/2))
+        *((1/(s*sqrt(2*pi)))*exp(-(1/(2*(s^2)))*((y-f)^2)))
+        """
+
+        #We want the variance around test points y which comes from int p(y*|f*)p(f*) df*
+        #Var(y*) = Var(E[y*|f*]) + E[Var(y*|f*)]
+        #Since we are given f* (mu) which is our mean (expected) value of y*|f* then the variance is the variance around this
+        #Which was also given to us as (var)
+        #We also need to know the expected variance of y* around samples f*, this is the variance of the student t distribution
+        #However the variance of the student t distribution is not dependent on f, only on sigma and the degrees of freedom
+        true_var = sigma**2 + self.variance
+
+        print "True var: {}".format(true_var)
+        return true_var
+
+    def _predictive_mean_analytical(self, mu, var):
+        """
+        Compute mean of the prediction
+        """
+        return mu
+
+    def sample_predicted_values(self, mu, var):
+        """ Experimental sample approches and numerical integration """
+        raise NotImplementedError
+        #p_025 = stats.t.ppf(.025, mu)
+        #p_975 = stats.t.ppf(.975, mu)
+
+        num_test_points = mu.shape[0]
+        #Each mu is the latent point f* at the test point x*,
+        #and the var is the gaussian variance at this point
+        #Take lots of samples from this, so we have lots of possible values
+        #for latent point f* for each test point x* weighted by how likely we were to pick it
+        print "Taking %d samples of f*".format(num_test_points)
+        num_f_samples = 10
+        num_y_samples = 10
+        student_t_means = np.random.normal(loc=mu, scale=np.sqrt(var), size=(num_test_points, num_f_samples))
+        print "Student t means shape: ", student_t_means.shape
+
+        #Now we have lots of f*, lets work out the likelihood of getting this by sampling
+        #from a student t centred on this point, sample many points from this distribution
+        #centred on f*
+        #for test_point, f in enumerate(student_t_means):
+            #print test_point
+            #print f.shape
+            #student_t_samples = stats.t.rvs(self.v, loc=f[:,None],
+                                            #scale=self.sigma,
+                                            #size=(num_f_samples, num_y_samples))
+            #print student_t_samples.shape
+
+        student_t_samples = stats.t.rvs(self.v, loc=student_t_means[:, None],
+                                        scale=self.sigma,
+                                        size=(num_test_points, num_y_samples, num_f_samples))
+        student_t_samples = np.reshape(student_t_samples,
+                                       (num_test_points, num_y_samples*num_f_samples))
+
+        #Now take the 97.5 and 0.25 percentile of these points
+        p_025 = stats.scoreatpercentile(student_t_samples, .025, axis=1)[:, None]
+        p_975 = stats.scoreatpercentile(student_t_samples, .975, axis=1)[:, None]
+
+        ##Alernenately we could sample from int p(y|f*)p(f*|x*) df*
+        def t_gaussian(f, mu, var):
+            return (((gamma((self.v+1)*0.5)) / (gamma(self.v*0.5)*self.sigma*np.sqrt(self.v*np.pi))) * ((1+(1/self.v)*(((mu-f)/self.sigma)**2))**(-(self.v+1)*0.5))
+                    * ((1/(np.sqrt(2*np.pi*var)))*np.exp(-(1/(2*var)) *((mu-f)**2)))
+                    )
+
+        def t_gauss_int(mu, var):
+            print "Mu: ", mu
+            print "var: ", var
+            result = integrate.quad(t_gaussian, 0.025, 0.975, args=(mu, var))
+            print "Result: ", result
+            return result[0]
+
+        vec_t_gauss_int = np.vectorize(t_gauss_int)
+
+        p = vec_t_gauss_int(mu, var)
+        p_025 = mu - p
+        p_975 = mu + p
+        return mu, np.nan*mu, p_025, p_975
+

GPy/mappings/mlp.py

@@ -10,11 +10,13 @@ class MLP(Mapping):
 
     .. math::
 
-       f(\mathbf{x}*) = \mathbf{W}^0\boldsymbol{\phi}(\mathbf{W}^1\mathbf{x}+\mathb{b}^1)^* + \mathbf{b}^0
+       f(\\mathbf{x}*) = \\mathbf{W}^0\\boldsymbol{\\phi}(\\mathbf{W}^1\\mathbf{x}+\\mathbf{b}^1)^* + \\mathbf{b}^0
 
     where
-    ..math::
+
-      \phi(\cdot) = \text{tanh}(\cdot)
+    .. math::
+
+      \\phi(\\cdot) = \\text{tanh}(\\cdot)
 
     :param X: input observations
     :type X: ndarray
@@ -22,6 +24,7 @@ class MLP(Mapping):
     :type output_dim: int
     :param hidden_dim: dimension of hidden layer. If it is an int, there is one hidden layer of the given dimension. If it is a list of ints there are as manny hidden layers as the length of the list, each with the given number of hidden nodes in it.
     :type hidden_dim: int or list of ints. 
+
     """
 
     def __init__(self, input_dim=1, output_dim=1, hidden_dim=3):

GPy/models/__init__.py

@@ -14,3 +14,5 @@ from warped_gp import WarpedGP
 from bayesian_gplvm import BayesianGPLVM
 from mrd import MRD
 from gradient_checker import GradientChecker
+from gp_multioutput_regression import GPMultioutputRegression
+from sparse_gp_multioutput_regression import SparseGPMultioutputRegression

GPy/models/bayesian_gplvm.py

@@ -8,7 +8,7 @@ from .. import kern
 import itertools
 from matplotlib.colors import colorConverter
 from GPy.inference.optimization import SCG
-from GPy.util import plot_latent
+from GPy.util import plot_latent, linalg
 from GPy.models.gplvm import GPLVM
 from GPy.util.plot_latent import most_significant_input_dimensions
 from matplotlib import pyplot
@@ -66,8 +66,8 @@ class BayesianGPLVM(SparseGP, GPLVM):
         S_names = sum([['X_variance_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], [])
         return (X_names + S_names + SparseGP._get_param_names(self))
 
-    def _get_print_names(self):
+    #def _get_print_names(self):
-        return SparseGP._get_print_names(self)
+    #    return SparseGP._get_print_names(self)
 
     def _get_params(self):
         """
@@ -140,12 +140,20 @@ class BayesianGPLVM(SparseGP, GPLVM):
         dpsi0 = -0.5 * self.input_dim * self.likelihood.precision
         dpsi2 = self.dL_dpsi2[0][None, :, :] # TODO: this may change if we ignore het. likelihoods
         V = self.likelihood.precision * Y
+
+        #compute CPsi1V
+        if self.Cpsi1V is None:
+            psi1V = np.dot(self.psi1.T, self.likelihood.V)
+            tmp, _ = linalg.dtrtrs(self._Lm, np.asfortranarray(psi1V), lower=1, trans=0)
+            tmp, _ = linalg.dpotrs(self.LB, tmp, lower=1)
+            self.Cpsi1V, _ = linalg.dtrtrs(self._Lm, tmp, lower=1, trans=1)
+
         dpsi1 = np.dot(self.Cpsi1V, V.T)
 
         start = np.zeros(self.input_dim * 2)
 
         for n, dpsi1_n in enumerate(dpsi1.T[:, :, None]):
-            args = (self.kern, self.Z, dpsi0, dpsi1_n, dpsi2)
+            args = (self.kern, self.Z, dpsi0, dpsi1_n.T, dpsi2)
             xopt, fopt, neval, status = SCG(f=latent_cost, gradf=latent_grad, x=start, optargs=args, display=False)
 
             mu, log_S = xopt.reshape(2, 1, -1)
@@ -237,12 +245,13 @@ class BayesianGPLVM(SparseGP, GPLVM):
         """
         Plot latent space X in 1D:
 
-            -if fig is given, create input_dim subplots in fig and plot in these
+            - if fig is given, create input_dim subplots in fig and plot in these
-            -if ax is given plot input_dim 1D latent space plots of X into each `axis`
+            - if ax is given plot input_dim 1D latent space plots of X into each `axis`
-            -if neither fig nor ax is given create a figure with fignum and plot in there
+            - if neither fig nor ax is given create a figure with fignum and plot in there
 
         colors:
             colors of different latent space dimensions input_dim
+
         """
         import pylab
         if ax is None:

GPy/models/bcgplvm.py

@@ -44,7 +44,7 @@ class BCGPLVM(GPLVM):
         GP._set_params(self, x[self.mapping.num_params:])
 
     def _log_likelihood_gradients(self):
-        dL_df = 2.*self.kern.dK_dX(self.dL_dK, self.X)
+        dL_df = self.kern.dK_dX(self.dL_dK, self.X)
         dL_dtheta = self.mapping.df_dtheta(dL_df, self.likelihood.Y)
         return np.hstack((dL_dtheta.flatten(), GP._log_likelihood_gradients(self)))
 

GPy/models/fitc_classification.py

@@ -31,8 +31,8 @@ class FITCClassification(FITC):
             kernel = kern.rbf(X.shape[1]) + kern.white(X.shape[1],1e-3)
 
         if likelihood is None:
-            distribution = likelihoods.likelihood_functions.Binomial()
+            noise_model = likelihoods.binomial()
-            likelihood = likelihoods.EP(Y, distribution)
+            likelihood = likelihoods.EP(Y, noise_model)
         elif Y is not None:
             if not all(Y.flatten() == likelihood.data.flatten()):
                 raise Warning, 'likelihood.data and Y are different.'

GPy/models/gp_classification.py

@@ -14,7 +14,7 @@ class GPClassification(GP):
     This is a thin wrapper around the models.GP class, with a set of sensible defaults
 
     :param X: input observations
-    :param Y: observed values
+    :param Y: observed values, can be None if likelihood is not None
     :param likelihood: a GPy likelihood, defaults to Binomial with probit link_function
     :param kernel: a GPy kernel, defaults to rbf
     :param normalize_X:  whether to normalize the input data before computing (predictions will be in original scales)
@@ -31,8 +31,8 @@ class GPClassification(GP):
             kernel = kern.rbf(X.shape[1])
 
         if likelihood is None:
-            distribution = likelihoods.likelihood_functions.Binomial()
+            noise_model = likelihoods.binomial()
-            likelihood = likelihoods.EP(Y, distribution)
+            likelihood = likelihoods.EP(Y, noise_model)
         elif Y is not None:
             if not all(Y.flatten() == likelihood.data.flatten()):
                 raise Warning, 'likelihood.data and Y are different.'

GPy/models/gp_multioutput_regression.py

@@ -0,0 +1,58 @@
+# Copyright (c) 2013, Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+from ..core import GP
+from .. import likelihoods
+from .. import kern
+
+class GPMultioutputRegression(GP):
+    """
+    Multiple output Gaussian process with Gaussian noise
+
+    This is a wrapper around the models.GP class, with a set of sensible defaults
+
+    :param X_list: input observations
+    :type X_list: list of numpy arrays (num_data_output_i x input_dim), one array per output
+    :param Y_list: observed values
+    :type Y_list: list of numpy arrays (num_data_output_i x 1), one array per output
+    :param kernel_list: GPy kernels, defaults to rbf
+    :type kernel_list: list of GPy kernels
+    :param noise_variance_list: noise parameters per output, defaults to 1.0 for every output
+    :type noise_variance_list: list of floats
+    :param normalize_X:  whether to normalize the input data before computing (predictions will be in original scales)
+    :type normalize_X: False|True
+    :param normalize_Y:  whether to normalize the input data before computing (predictions will be in original scales)
+    :type normalize_Y: False|True
+    :param rank: number tuples of the corregionalization parameters 'coregion_W' (see coregionalize kernel documentation)
+    :type rank: integer
+    """
+
+    def __init__(self,X_list,Y_list,kernel_list=None,noise_variance_list=None,normalize_X=False,normalize_Y=False,rank=1):
+
+        self.output_dim = len(Y_list)
+        assert len(X_list) == self.output_dim, 'Number of outputs do not match length of inputs list.'
+
+        #Inputs indexing
+        i = 0
+        index = []
+        for x,y in zip(X_list,Y_list):
+            assert x.shape[0] == y.shape[0]
+            index.append(np.repeat(i,x.size)[:,None])
+            i += 1
+        index = np.vstack(index)
+        X = np.hstack([np.vstack(X_list),index])
+        original_dim = X.shape[1] - 1
+
+        #Mixed noise likelihood definition
+        likelihood = likelihoods.Gaussian_Mixed_Noise(Y_list,noise_params=noise_variance_list,normalize=normalize_Y)
+
+        #Coregionalization kernel definition
+        if kernel_list is None:
+            kernel_list = [kern.rbf(original_dim)]
+        mkernel = kern.build_lcm(input_dim=original_dim, output_dim=self.output_dim, kernel_list = kernel_list, rank=rank)
+
+        self.multioutput = True
+        GP.__init__(self, X, likelihood, mkernel, normalize_X=normalize_X)
+        self.ensure_default_constraints()

GPy/models/gplvm.py

@@ -61,7 +61,7 @@ class GPLVM(GP):
         GP._set_params(self, x[self.X.size:])
 
     def _log_likelihood_gradients(self):
-        dL_dX = 2.*self.kern.dK_dX(self.dL_dK, self.X)
+        dL_dX = self.kern.dK_dX(self.dL_dK, self.X)
 
         return np.hstack((dL_dX.flatten(), GP._log_likelihood_gradients(self)))
 

GPy/models/mrd.py

@@ -39,6 +39,7 @@ class MRD(Model):
     :param num_inducing: number of inducing inputs to use
     :param kernels: list of kernels or kernel shared for all BGPLVMS
     :type kernels: [GPy.kern.kern] | GPy.kern.kern | None (default)
+
     """
     def __init__(self, likelihood_or_Y_list, input_dim, num_inducing=10, names=None,
                  kernels=None, initx='PCA',
@@ -163,28 +164,31 @@ class MRD(Model):
         self._init_X(initx, self.likelihood_list)
         self._init_Z(initz, self.X)
 
-    def _get_latent_param_names(self):
+    #def _get_latent_param_names(self):
+    def _get_param_names(self):
         n1 = self.gref._get_param_names()
         n1var = n1[:self.NQ * 2 + self.MQ]
-        return n1var
+    #    return n1var
-
+    #
-
+    #def _get_kernel_names(self):
-    def _get_kernel_names(self):
         map_names = lambda ns, name: map(lambda x: "{1}_{0}".format(*x),
                                          itertools.izip(ns,
                                                         itertools.repeat(name)))
-        kernel_names = (map_names(SparseGP._get_param_names(g)[self.MQ:], n) for g, n in zip(self.bgplvms, self.names))
+        return list(itertools.chain(n1var, *(map_names(\
-        return kernel_names
+                SparseGP._get_param_names(g)[self.MQ:], n) \
+                for g, n in zip(self.bgplvms, self.names))))
+    #    kernel_names = (map_names(SparseGP._get_param_names(g)[self.MQ:], n) for g, n in zip(self.bgplvms, self.names))
+    #    return kernel_names
 
-    def _get_param_names(self):
+    #def _get_param_names(self):
         # X_names = sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], [])
         # S_names = sum([['X_variance_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], [])
-        n1var = self._get_latent_param_names()
+    #    n1var = self._get_latent_param_names()
-        kernel_names = self._get_kernel_names()
+    #    kernel_names = self._get_kernel_names()
-        return list(itertools.chain(n1var, *kernel_names))
+    #    return list(itertools.chain(n1var, *kernel_names))
 
-    def _get_print_names(self):
+    #def _get_print_names(self):
-        return list(itertools.chain(*self._get_kernel_names()))
+    #    return list(itertools.chain(*self._get_kernel_names()))
 
     def _get_params(self):
         """
@@ -335,8 +339,11 @@ class MRD(Model):
 
     def plot_scales(self, fignum=None, ax=None, titles=None, sharex=False, sharey=True, *args, **kwargs):
         """
-        :param:`titles` :
+
-            titles for axes of datasets
+        TODO: Explain other parameters
+
+        :param titles: titles for axes of datasets
+
         """
         if titles is None:
             titles = [r'${}$'.format(name) for name in self.names]

GPy/models/sparse_gp_classification.py

@@ -28,11 +28,11 @@ class SparseGPClassification(SparseGP):
 
     def __init__(self, X, Y=None, likelihood=None, kernel=None, normalize_X=False, normalize_Y=False, Z=None, num_inducing=10):
         if kernel is None:
-            kernel = kern.rbf(X.shape[1]) + kern.white(X.shape[1], 1e-3)
+            kernel = kern.rbf(X.shape[1])# + kern.white(X.shape[1],1e-3)
 
         if likelihood is None:
-            distribution = likelihoods.likelihood_functions.Binomial()
+            noise_model = likelihoods.binomial()
-            likelihood = likelihoods.EP(Y, distribution)
+            likelihood = likelihoods.EP(Y, noise_model)
         elif Y is not None:
             if not all(Y.flatten() == likelihood.data.flatten()):
                 raise Warning, 'likelihood.data and Y are different.'

GPy/models/sparse_gp_multioutput_regression.py

@@ -0,0 +1,80 @@
+# Copyright (c) 2013, Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+import numpy as np
+from ..core import SparseGP
+from .. import likelihoods
+from .. import kern
+from ..util import multioutput
+
+class SparseGPMultioutputRegression(SparseGP):
+    """
+    Sparse multiple output Gaussian process with Gaussian noise
+
+    This is a wrapper around the models.SparseGP class, with a set of sensible defaults
+
+    :param X_list: input observations
+    :type X_list: list of numpy arrays (num_data_output_i x input_dim), one array per output
+    :param Y_list: observed values
+    :type Y_list: list of numpy arrays (num_data_output_i x 1), one array per output
+    :param kernel_list: GPy kernels, defaults to rbf
+    :type kernel_list: list of GPy kernels
+    :param noise_variance_list: noise parameters per output, defaults to 1.0 for every output
+    :type noise_variance_list: list of floats
+    :param normalize_X:  whether to normalize the input data before computing (predictions will be in original scales)
+    :type normalize_X: False|True
+    :param normalize_Y:  whether to normalize the input data before computing (predictions will be in original scales)
+    :type normalize_Y: False|True
+    :param Z_list: inducing inputs (optional)
+    :type Z_list: list of numpy arrays (num_inducing_output_i x input_dim), one array per output | empty list
+    :param num_inducing: number of inducing inputs per output, defaults to 10 (ignored if Z_list is not empty)
+    :type num_inducing: integer
+    :param rank: number tuples of the corregionalization parameters 'coregion_W' (see coregionalize kernel documentation)
+    :type rank: integer
+    """
+    #NOTE not tested with uncertain inputs
+    def __init__(self,X_list,Y_list,kernel_list=None,noise_variance_list=None,normalize_X=False,normalize_Y=False,Z_list=[],num_inducing=10,rank=1):
+
+        self.output_dim = len(Y_list)
+        assert len(X_list) == self.output_dim, 'Number of outputs do not match length of inputs list.'
+
+        #Inducing inputs list
+        if len(Z_list):
+            assert len(Z_list) == self.output_dim, 'Number of outputs do not match length of inducing inputs list.'
+        else:
+            if isinstance(num_inducing,np.int):
+                num_inducing = [num_inducing] * self.output_dim
+            num_inducing = np.asarray(num_inducing)
+            assert num_inducing.size == self.output_dim, 'Number of outputs do not match length of inducing inputs list.'
+            for ni,X in zip(num_inducing,X_list):
+                i = np.random.permutation(X.shape[0])[:ni]
+                Z_list.append(X[i].copy())
+
+        #Inputs and inducing inputs indexing
+        i = 0
+        index = []
+        index_z = []
+        for x,y,z in zip(X_list,Y_list,Z_list):
+            assert x.shape[0] == y.shape[0]
+            index.append(np.repeat(i,x.size)[:,None])
+            index_z.append(np.repeat(i,z.size)[:,None])
+            i += 1
+        index = np.vstack(index)
+        index_z = np.vstack(index_z)
+        X = np.hstack([np.vstack(X_list),index])
+        Z = np.hstack([np.vstack(Z_list),index_z])
+        original_dim = X.shape[1] - 1
+
+        #Mixed noise likelihood definition
+        likelihood = likelihoods.Gaussian_Mixed_Noise(Y_list,noise_params=noise_variance_list,normalize=normalize_Y)
+
+        #Coregionalization kernel definition
+        if kernel_list is None:
+            kernel_list = [kern.rbf(original_dim)]
+        mkernel = kern.build_lcm(input_dim=original_dim, output_dim=self.output_dim, kernel_list = kernel_list, rank=rank)
+
+        self.multioutput = True
+        SparseGP.__init__(self, X, likelihood, mkernel, Z=Z, normalize_X=normalize_X)
+        self.constrain_fixed('.*iip_\d+_1')
+        self.ensure_default_constraints()

GPy/models/sparse_gp_regression.py

@@ -20,7 +20,11 @@ class SparseGPRegression(SparseGP):
     :type normalize_X: False|True
     :param normalize_Y:  whether to normalize the input data before computing (predictions will be in original scales)
     :type normalize_Y: False|True
+    :param Z: inducing inputs (optional, see note)
+    :type Z: np.ndarray (num_inducing x input_dim) | None
     :rtype: model object
+    :param X_variance: The uncertainty in the measurements of X (Gaussian variance)
+    :type X_variance: np.ndarray (num_data x input_dim) | None
 
     .. Note:: Multiple independent outputs are allowed using columns of Y
 

GPy/notes.txt

@@ -38,7 +38,7 @@ In sparse GPs wouldn't it be clearer to call Z inducing?
 
 In coregionalisation matrix, setting the W to all ones will (surely?) ensure that symmetry isn't broken. Also, but allowing it to scale like that, the output variance increases as rank is increased (and if user sets rank to more than output dim they could get very different results).
 
-We are inconsistent about our use of ise and ize e.g. optimize and normalize_X, but coregionalise, we should choose one and stick to it. Suggest -ize.
+We are inconsistent about our use of ise and ize e.g. optimize and normalize_X, but coregionalise, we should choose one and stick to it. Suggest -ize. Neil- I'm imposing the US spellings to keep things consistent, so -ize it is.
 
 Exceptions: we need to provide a list of exceptions we throw and specify what is thrown where. 
 

GPy/testing/bcgplvm_tests.py

@@ -0,0 +1,50 @@
+# Copyright (c) 2013, GPy authors (see AUTHORS.txt)
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import unittest
+import numpy as np
+import GPy
+
+class BCGPLVMTests(unittest.TestCase):
+    def test_kernel_backconstraint(self):
+        num_data, num_inducing, input_dim, output_dim = 10, 3, 2, 4
+        X = np.random.rand(num_data, input_dim)
+        k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
+        K = k.K(X)
+        Y = np.random.multivariate_normal(np.zeros(num_data),K,output_dim).T
+        k = GPy.kern.mlp(input_dim) + GPy.kern.bias(input_dim)
+        bk = GPy.kern.rbf(output_dim)
+        mapping = GPy.mappings.Kernel(output_dim=input_dim, X=Y, kernel=bk)
+        m = GPy.models.BCGPLVM(Y, input_dim, kernel = k, mapping=mapping)
+        m.randomize()
+        self.assertTrue(m.checkgrad())
+        
+    def test_linear_backconstraint(self):
+        num_data, num_inducing, input_dim, output_dim = 10, 3, 2, 4
+        X = np.random.rand(num_data, input_dim)
+        k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
+        K = k.K(X)
+        Y = np.random.multivariate_normal(np.zeros(num_data),K,output_dim).T
+        k = GPy.kern.mlp(input_dim) + GPy.kern.bias(input_dim)
+        bk = GPy.kern.rbf(output_dim)
+        mapping = GPy.mappings.Linear(output_dim=input_dim, input_dim=output_dim)
+        m = GPy.models.BCGPLVM(Y, input_dim, kernel = k, mapping=mapping)
+        m.randomize()
+        self.assertTrue(m.checkgrad())
+        
+    def test_mlp_backconstraint(self):
+        num_data, num_inducing, input_dim, output_dim = 10, 3, 2, 4
+        X = np.random.rand(num_data, input_dim)
+        k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
+        K = k.K(X)
+        Y = np.random.multivariate_normal(np.zeros(num_data),K,output_dim).T
+        k = GPy.kern.mlp(input_dim) + GPy.kern.bias(input_dim)
+        bk = GPy.kern.rbf(output_dim)
+        mapping = GPy.mappings.MLP(output_dim=input_dim, input_dim=output_dim, hidden_dim=[5, 4, 7])
+        m = GPy.models.BCGPLVM(Y, input_dim, kernel = k, mapping=mapping)
+        m.randomize()
+        self.assertTrue(m.checkgrad())
+
+if __name__ == "__main__":
+    print "Running unit tests, please be (very) patient..."
+    unittest.main()

GPy/testing/bgplvm_tests.py

@@ -55,7 +55,18 @@ class BGPLVMTests(unittest.TestCase):
         m.randomize()
         self.assertTrue(m.checkgrad())
 
-    #@unittest.skip('psi2 cross terms are NotImplemented for this combination')
+    def test_rbf_line_kern(self):
+        N, num_inducing, input_dim, D = 10, 3, 2, 4
+        X = np.random.rand(N, input_dim)
+        k = GPy.kern.rbf(input_dim) +  GPy.kern.linear(input_dim) + GPy.kern.white(input_dim, 0.00001)
+        K = k.K(X)
+        Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
+        Y -= Y.mean(axis=0)
+        k = GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001)
+        m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing)
+        m.randomize()
+        self.assertTrue(m.checkgrad())
+
     def test_linear_bias_kern(self):
         N, num_inducing, input_dim, D = 30, 5, 4, 30
         X = np.random.rand(N, input_dim)

GPy/testing/kernel_tests.py

@@ -5,39 +5,71 @@ import unittest
 import numpy as np
 import GPy
 
-
+verbose = False
 
 class KernelTests(unittest.TestCase):
     def test_kerneltie(self):
         K = GPy.kern.rbf(5, ARD=True)
         K.tie_params('.*[01]')
         K.constrain_fixed('2')
-        
         X = np.random.rand(5,5)
         Y = np.ones((5,1))
         m = GPy.models.GPRegression(X,Y,K)
         self.assertTrue(m.checkgrad())
 
     def test_rbfkernel(self):
-        verbose = False
         kern = GPy.kern.rbf(5)
-        self.assertTrue(GPy.kern.Kern_check_model(kern).is_positive_definite())
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
-        self.assertTrue(GPy.kern.Kern_check_dK_dtheta(kern).checkgrad(verbose=verbose))
+
-        self.assertTrue(GPy.kern.Kern_check_dKdiag_dtheta(kern).checkgrad(verbose=verbose))
+    def test_rbf_sympykernel(self):
-        self.assertTrue(GPy.kern.Kern_check_dK_dX(kern).checkgrad(verbose=verbose))
+        kern = GPy.kern.rbf_sympy(5)
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
+
+    def test_rbf_invkernel(self):
+        kern = GPy.kern.rbf_inv(5)
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
+
+    def test_Matern32kernel(self):
+        kern = GPy.kern.Matern32(5)
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
+
+    def test_Matern52kernel(self):
+        kern = GPy.kern.Matern52(5)
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
+
+    def test_linearkernel(self):
+        kern = GPy.kern.linear(5)
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
+
+    def test_periodic_exponentialkernel(self):
+        kern = GPy.kern.periodic_exponential(1)
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
+
+    def test_periodic_Matern32kernel(self):
+        kern = GPy.kern.periodic_Matern32(1)
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
+
+    def test_periodic_Matern52kernel(self):
+        kern = GPy.kern.periodic_Matern52(1)
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
+
+    def test_rational_quadratickernel(self):
+        kern = GPy.kern.rational_quadratic(1)
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
 
     def test_gibbskernel(self):
-        verbose = False
         kern = GPy.kern.gibbs(5, mapping=GPy.mappings.Linear(5, 1))
         self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
 
+    def test_heterokernel(self):
+        kern = GPy.kern.hetero(5, mapping=GPy.mappings.Linear(5, 1), transform=GPy.core.transformations.logexp())
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
+
     def test_mlpkernel(self):
-        verbose = False
         kern = GPy.kern.mlp(5)
         self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
 
     def test_polykernel(self):
-        verbose = False
         kern = GPy.kern.poly(5, degree=4)
         self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
 
@@ -48,25 +80,22 @@ class KernelTests(unittest.TestCase):
         X = np.random.rand(30, 4)
         K = np.dot(X, X.T)
         kernel = GPy.kern.fixed(4, K)
-        Y = np.ones((30,1))
+        kern = GPy.kern.poly(5, degree=4)
-        m = GPy.models.GPRegression(X,Y,kernel=kernel)
+        self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
-        self.assertTrue(m.checkgrad())
 
-    def test_coregionalisation(self):
+    # def test_coregionalization(self):
-        X1 = np.random.rand(50,1)*8
+    #     X1 = np.random.rand(50,1)*8
-        X2 = np.random.rand(30,1)*5
+    #     X2 = np.random.rand(30,1)*5
-        index = np.vstack((np.zeros_like(X1),np.ones_like(X2)))
+    #     index = np.vstack((np.zeros_like(X1),np.ones_like(X2)))
-        X = np.hstack((np.vstack((X1,X2)),index))
+    #     X = np.hstack((np.vstack((X1,X2)),index))
-        Y1 = np.sin(X1) + np.random.randn(*X1.shape)*0.05
+    #     Y1 = np.sin(X1) + np.random.randn(*X1.shape)*0.05
-        Y2 = np.sin(X2) + np.random.randn(*X2.shape)*0.05 + 2.
+    #     Y2 = np.sin(X2) + np.random.randn(*X2.shape)*0.05 + 2.
-        Y = np.vstack((Y1,Y2))
+    #     Y = np.vstack((Y1,Y2))
-
-        k1 = GPy.kern.rbf(1) + GPy.kern.bias(1)
-        k2 = GPy.kern.coregionalise(2,1)
-        k = k1.prod(k2,tensor=True)
-        m = GPy.models.GPRegression(X,Y,kernel=k)
-        self.assertTrue(m.checkgrad())
 
+    #     k1 = GPy.kern.rbf(1) + GPy.kern.bias(1)
+    #     k2 = GPy.kern.coregionalize(2,1)
+    #     kern = k1**k2
+    #     self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
 
 
 if __name__ == "__main__":

GPy/testing/laplace_tests.py

@@ -72,14 +72,17 @@ class LaplaceTests(unittest.TestCase):
         noise = np.random.randn(*self.X.shape)*self.real_std
         self.Y = np.sin(self.X*2*np.pi) + noise
         #self.Y = np.array([[1.0]])#np.sin(self.X*2*np.pi) + noise
-        self.var = 0.3
+        self.var = 0.2
 
         self.f = np.random.rand(self.N, self.D)
         #self.f = np.array([[3.0]])#np.sin(self.X*2*np.pi) + noise
 
         self.var = np.random.rand(1)
-        self.stu_t = GPy.likelihoods.functions.StudentT(deg_free=5, sigma2=self.var)
+        self.stu_t = GPy.likelihoods.student_t(deg_free=5, sigma2=self.var)
-        self.gauss = GPy.likelihoods.functions.Gaussian(self.var, self.D, self.N)
+        self.gauss = GPy.likelihoods.gaussian(variance=self.var, D=self.D, N=self.N)
+
+        #Make a bigger step as lower bound can be quite curved
+        self.step = 1e-4
 
     def tearDown(self):
         self.stu_t = None
@@ -118,7 +121,7 @@ class LaplaceTests(unittest.TestCase):
         noise = np.random.randn(*self.X.shape)*self.real_std
         self.Y = np.sin(self.X*2*np.pi) + noise
         self.f = np.random.rand(self.N, 1)
-        self.gauss = GPy.likelihoods.functions.Gaussian(self.var, self.D, self.N)
+        self.gauss = GPy.likelihoods.gaussian(variance=self.var, D=self.D, N=self.N)
 
         dlik_df = functools.partial(self.gauss.dlik_df, self.Y)
         d2lik_d2f = functools.partial(self.gauss.d2lik_d2f, self.Y)
@@ -167,6 +170,7 @@ class LaplaceTests(unittest.TestCase):
         grad = GradientChecker(link, dlik_df, self.f.copy(), 'f')
         grad.randomize()
         grad.checkgrad(verbose=1)
+        self.assertTrue(grad.checkgrad())
 
     def test_studentt_d2lik_d2f(self):
         print "\n{}".format(inspect.stack()[0][3])
@@ -175,6 +179,7 @@ class LaplaceTests(unittest.TestCase):
         grad = GradientChecker(dlik_df, d2lik_d2f, self.f.copy(), 'f')
         grad.randomize()
         grad.checkgrad(verbose=1)
+        self.assertTrue(grad.checkgrad())
 
     def test_studentt_d3lik_d3f(self):
         print "\n{}".format(inspect.stack()[0][3])
@@ -183,6 +188,7 @@ class LaplaceTests(unittest.TestCase):
         grad = GradientChecker(d2lik_d2f, d3lik_d3f, self.f.copy(), 'f')
         grad.randomize()
         grad.checkgrad(verbose=1)
+        self.assertTrue(grad.checkgrad())
 
     def test_studentt_dlik_dvar(self):
         print "\n{}".format(inspect.stack()[0][3])
@@ -216,27 +222,27 @@ class LaplaceTests(unittest.TestCase):
         m = GPy.models.GPRegression(self.X, self.Y.copy(), kernel, likelihood=gauss_laplace)
         m.ensure_default_constraints()
         m.randomize()
-        m.checkgrad(verbose=1)
+        m.checkgrad(verbose=1, step=self.step)
-        self.assertTrue(m.checkgrad())
+        self.assertTrue(m.checkgrad(step=self.step))
 
     def test_studentt_approx_gauss_rbf(self):
         print "\n{}".format(inspect.stack()[0][3])
         self.Y = self.Y/self.Y.max()
-        self.stu_t = GPy.likelihoods.functions.StudentT(deg_free=1000, sigma2=self.var)
+        self.stu_t = GPy.likelihoods.student_t(deg_free=1000, sigma2=self.var)
         kernel = GPy.kern.rbf(self.X.shape[1]) + GPy.kern.white(self.X.shape[1])
         stu_t_laplace = GPy.likelihoods.Laplace(self.Y.copy(), self.stu_t, opt='rasm')
         m = GPy.models.GPRegression(self.X, self.Y.copy(), kernel, likelihood=stu_t_laplace)
         m.ensure_default_constraints()
         m.constrain_positive('t_noise')
         m.randomize()
-        m.checkgrad(verbose=1)
+        m.checkgrad(verbose=1, step=self.step)
         print m
-        self.assertTrue(m.checkgrad())
+        self.assertTrue(m.checkgrad(step=self.step))
 
     def test_studentt_rbf(self):
         print "\n{}".format(inspect.stack()[0][3])
         self.Y = self.Y/self.Y.max()
-        white_var = 3.0
+        white_var = 1
         kernel = GPy.kern.rbf(self.X.shape[1]) + GPy.kern.white(self.X.shape[1])
         stu_t_laplace = GPy.likelihoods.Laplace(self.Y.copy(), self.stu_t, opt='rasm')
         m = GPy.models.GPRegression(self.X, self.Y.copy(), kernel, likelihood=stu_t_laplace)
@@ -244,14 +250,14 @@ class LaplaceTests(unittest.TestCase):
         m.constrain_positive('t_noise')
         m.constrain_fixed('white', white_var)
         m.randomize()
-        m.checkgrad(verbose=1)
+        m.checkgrad(verbose=1, step=self.step)
         print m
-        self.assertTrue(m.checkgrad())
+        self.assertTrue(m.checkgrad(step=self.step))
 
     def test_studentt_rbf_smallvar(self):
         print "\n{}".format(inspect.stack()[0][3])
         self.Y = self.Y/self.Y.max()
-        white_var = 3.0
+        white_var = 1
         kernel = GPy.kern.rbf(self.X.shape[1]) + GPy.kern.white(self.X.shape[1])
         stu_t_laplace = GPy.likelihoods.Laplace(self.Y.copy(), self.stu_t, opt='rasm')
         m = GPy.models.GPRegression(self.X, self.Y.copy(), kernel, likelihood=stu_t_laplace)
@@ -259,9 +265,9 @@ class LaplaceTests(unittest.TestCase):
         m.constrain_positive('t_noise')
         m.constrain_fixed('white', white_var)
         m['t_noise'] = 0.01
-        m.checkgrad(verbose=1)
+        m.checkgrad(verbose=1, step=self.step)
         print m
-        self.assertTrue(m.checkgrad())
+        self.assertTrue(m.checkgrad(step=self.step))
 
 if __name__ == "__main__":
     print "Running unit tests"

GPy/testing/unit_tests.py

@@ -5,7 +5,6 @@
 import unittest
 import numpy as np
 import GPy
-from GPy.likelihoods.likelihood_functions import Binomial
 
 class GradientTests(unittest.TestCase):
     def setUp(self):
@@ -199,10 +198,7 @@ class GradientTests(unittest.TestCase):
         X = np.hstack([np.random.normal(5, 2, N / 2), np.random.normal(10, 2, N / 2)])[:, None]
         Y = np.hstack([np.ones(N / 2), np.zeros(N / 2)])[:, None]
         kernel = GPy.kern.rbf(1)
-        distribution = GPy.likelihoods.likelihood_functions.Binomial()
+        m = GPy.models.GPClassification(X,Y,kernel=kernel)
-        likelihood = GPy.likelihoods.EP(Y, distribution)
-        m = GPy.core.GP(X, likelihood, kernel)
-        m.ensure_default_constraints()
         m.update_likelihood_approximation()
         self.assertTrue(m.checkgrad())
 
@@ -212,10 +208,11 @@ class GradientTests(unittest.TestCase):
         Y = np.hstack([np.ones(N / 2), np.zeros(N / 2)])[:, None]
         Z = np.linspace(0, 15, 4)[:, None]
         kernel = GPy.kern.rbf(1)
-        distribution = GPy.likelihoods.likelihood_functions.Binomial()
+        m = GPy.models.SparseGPClassification(X,Y,kernel=kernel,Z=Z)
-        likelihood = GPy.likelihoods.EP(Y, distribution)
+        #distribution = GPy.likelihoods.likelihood_functions.Binomial()
-        m = GPy.core.SparseGP(X, likelihood, kernel, Z)
+        #likelihood = GPy.likelihoods.EP(Y, distribution)
-        m.ensure_default_constraints()
+        #m = GPy.core.SparseGP(X, likelihood, kernel, Z)
+        #m.ensure_default_constraints()
         m.update_likelihood_approximation()
         self.assertTrue(m.checkgrad())
 
@@ -224,10 +221,36 @@ class GradientTests(unittest.TestCase):
         X = np.hstack([np.random.rand(N / 2) + 1, np.random.rand(N / 2) - 1])[:, None]
         k = GPy.kern.rbf(1) + GPy.kern.white(1)
         Y = np.hstack([np.ones(N/2),np.zeros(N/2)])[:,None]
-        m = GPy.models.FITCClassification(X, Y=Y)
+        m = GPy.models.FITCClassification(X, Y, kernel = k)
         m.update_likelihood_approximation()
         self.assertTrue(m.checkgrad())
 
+    def multioutput_regression_1D(self):
+        X1 = np.random.rand(50, 1) * 8
+        X2 = np.random.rand(30, 1) * 5
+        X = np.vstack((X1, X2))
+        Y1 = np.sin(X1) + np.random.randn(*X1.shape) * 0.05
+        Y2 = -np.sin(X2) + np.random.randn(*X2.shape) * 0.05
+        Y = np.vstack((Y1, Y2))
+
+        k1 = GPy.kern.rbf(1)
+        m = GPy.models.GPMultioutputRegression(X_list=[X1,X2],Y_list=[Y1,Y2],kernel_list=[k1])
+        m.constrain_fixed('.*rbf_var', 1.)
+        self.assertTrue(m.checkgrad())
+
+    def multioutput_sparse_regression_1D(self):
+        X1 = np.random.rand(500, 1) * 8
+        X2 = np.random.rand(300, 1) * 5
+        X = np.vstack((X1, X2))
+        Y1 = np.sin(X1) + np.random.randn(*X1.shape) * 0.05
+        Y2 = -np.sin(X2) + np.random.randn(*X2.shape) * 0.05
+        Y = np.vstack((Y1, Y2))
+
+        k1 = GPy.kern.rbf(1)
+        m = GPy.models.SparseGPMultioutputRegression(X_list=[X1,X2],Y_list=[Y1,Y2],kernel_list=[k1])
+        m.constrain_fixed('.*rbf_var', 1.)
+        self.assertTrue(m.checkgrad())
+
 if __name__ == "__main__":
     print "Running unit tests, please be (very) patient..."
     unittest.main()

GPy/util/datasets.py

@@ -8,8 +8,20 @@ import zipfile
 import tarfile
 import datetime
 
+ipython_notebook = False
+if ipython_notebook:
+    import IPython.core.display
+    def ipynb_input(varname, prompt=''):
+        """Prompt user for input and assign string val to given variable name."""
+        js_code = ("""
+            var value = prompt("{prompt}","");
+            var py_code = "{varname} = '" + value + "'";
+            IPython.notebook.kernel.execute(py_code);
+        """).format(prompt=prompt, varname=varname)
+        return IPython.core.display.Javascript(js_code)
 
 import sys, urllib
+
 def reporthook(a,b,c): 
     # ',' at the end of the line is important!
     #print "% 3.1f%% of %d bytes\r" % (min(100, float(a * b) / c * 100), c),
@@ -131,12 +143,16 @@ The database was created with funding from NSF EIA-0196217.""",
                                         'size' : 24229368},
                   }
 
+
 def prompt_user():
     """Ask user for agreeing to data set licenses."""
     # raw_input returns the empty string for "enter"
     yes = set(['yes', 'y'])
     no = set(['no','n'])
-
+    choice = ''
+    if ipython_notebook:
+        ipynb_input(choice, prompt='provide your answer here')
+    else:
         choice = raw_input().lower()
     if choice in yes:
         return True
@@ -146,6 +162,7 @@ def prompt_user():
         sys.stdout.write("Please respond with 'yes', 'y' or 'no', 'n'")
         return prompt_user()
 
+
 def data_available(dataset_name=None):
     """Check if the data set is available on the local machine already."""
     for file_list in data_resources[dataset_name]['files']:
@@ -524,11 +541,14 @@ def simulation_BGPLVM():
             'info': "Simulated test dataset generated in MATLAB to compare BGPLVM between python and MATLAB"}
 
 def toy_rbf_1d(seed=default_seed, num_samples=500):
-    """Samples values of a function from an RBF covariance with very small noise for inputs uniformly distributed between -1 and 1.
+    """
+    Samples values of a function from an RBF covariance with very small noise for inputs uniformly distributed between -1 and 1.
+
     :param seed: seed to use for random sampling.
     :type seed: int
     :param num_samples: number of samples to sample in the function (default 500).
     :type num_samples: int
+
     """
     np.random.seed(seed=seed)
     num_in = 1
@@ -631,11 +651,15 @@ def olympic_marathon_men(data_set='olympic_marathon_men'):
 
 
 def crescent_data(num_data=200, seed=default_seed):
-    """Data set formed from a mixture of four Gaussians. In each class two of the Gaussians are elongated at right angles to each other and offset to form an approximation to the crescent data that is popular in semi-supervised learning as a toy problem.
+    """
+Data set formed from a mixture of four Gaussians. In each class two of the Gaussians are elongated at right angles to each other and offset to form an approximation to the crescent data that is popular in semi-supervised learning as a toy problem.
+
     :param num_data_part: number of data to be sampled (default is 200).
     :type num_data: int
     :param seed: random seed to be used for data generation.
-    :type seed: int"""
+    :type seed: int
+
+    """
     np.random.seed(seed=seed)
     sqrt2 = np.sqrt(2)
     # Rotation matrix

GPy/util/erfcx.py

@@ -0,0 +1,63 @@
+## Copyright (C) 2010 Soren Hauberg
+##
+## Copyright James Hensman 2011
+## 
+## This program is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or (at
+## your option) any later version.
+##
+## This program is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+import numpy as np
+
+def erfcx (arg):
+	arg = np.atleast_1d(arg)
+	assert(np.all(np.isreal(arg)),"erfcx: input must be real")
+
+	## Get precision dependent thresholds -- or not :p
+	xneg = -26.628;
+	xmax = 2.53e+307;
+
+	## Allocate output
+	result = np.zeros (arg.shape)
+
+	## Find values where erfcx can be evaluated
+	idx_neg = (arg < xneg);
+	idx_max = (arg > xmax);
+	idx = ~(idx_neg | idx_max);
+
+	arg = arg [idx];
+
+	## Perform the actual computation
+	t = 3.97886080735226 / (np.abs (arg) + 3.97886080735226);
+	u = t - 0.5;
+	y = (((((((((u * 0.00127109764952614092 + 1.19314022838340944e-4) * u \
+	    - 0.003963850973605135)   * u - 8.70779635317295828e-4) * u +     \
+	      0.00773672528313526668) * u + 0.00383335126264887303) * u -     \
+	      0.0127223813782122755)  * u - 0.0133823644533460069)  * u +     \
+	      0.0161315329733252248)  * u + 0.0390976845588484035)  * u +     \
+	      0.00249367200053503304;
+	y = ((((((((((((y * u - 0.0838864557023001992) * u -           \
+	      0.119463959964325415) * u + 0.0166207924969367356) * u + \
+	      0.357524274449531043) * u + 0.805276408752910567)  * u + \
+	      1.18902982909273333)  * u + 1.37040217682338167)   * u + \
+	      1.31314653831023098)  * u + 1.07925515155856677)   * u + \
+	      0.774368199119538609) * u + 0.490165080585318424)  * u + \
+	      0.275374741597376782) * t;
+
+	y [arg < 0] = 2 * np.exp (arg [arg < 0]**2) - y [arg < 0];
+
+	## Put the results back into something with the same size is the original input
+	result [idx] = y;
+	result [idx_neg] = np.inf;
+	## result (idx_max) = 0; # not needed as we initialise with zeros
+	return(result)
+

GPy/util/linalg.py

@@ -27,31 +27,37 @@ except:
     _blas_available = False
 
 def dtrtrs(A, B, lower=0, trans=0, unitdiag=0):
-    """Wrapper for lapack dtrtrs function
+    """
+    Wrapper for lapack dtrtrs function
 
     :param A: Matrix A
     :param B: Matrix B
     :param lower: is matrix lower (true) or upper (false)
     :returns:
+
     """
     return lapack.dtrtrs(A, B, lower=lower, trans=trans, unitdiag=unitdiag)
 
 def dpotrs(A, B, lower=0):
-    """Wrapper for lapack dpotrs function
+    """
+    Wrapper for lapack dpotrs function
 
     :param A: Matrix A
     :param B: Matrix B
     :param lower: is matrix lower (true) or upper (false)
     :returns:
+
     """
     return lapack.dpotrs(A, B, lower=lower)
 
 def dpotri(A, lower=0):
-    """Wrapper for lapack dpotri function
+    """
+    Wrapper for lapack dpotri function
 
     :param A: Matrix A
     :param lower: is matrix lower (true) or upper (false)
-    :returns:
+    :returns: A inverse
+
     """
     return lapack.dpotri(A, lower=lower)
 
@@ -65,18 +71,20 @@ def pddet(A):
 
 def trace_dot(a, b):
     """
-    efficiently compute the trace of the matrix product of a and b
+    Efficiently compute the trace of the matrix product of a and b
     """
     return np.sum(a * b)
 
 def mdot(*args):
-    """Multiply all the arguments using matrix product rules.
+    """
+    Multiply all the arguments using matrix product rules.
     The output is equivalent to multiplying the arguments one by one
     from left to right using dot().
     Precedence can be controlled by creating tuples of arguments,
     for instance mdot(a,((b,c),d)) multiplies a (a*((b*c)*d)).
     Note that this means the output of dot(a,b) and mdot(a,b) will differ if
     a or b is a pure tuple of numbers.
+
     """
     if len(args) == 1:
         return args[0]
@@ -123,14 +131,16 @@ def jitchol(A, maxtries=5):
 
 def jitchol_old(A, maxtries=5):
     """
-    :param A : An almost pd square matrix
+    :param A: An almost pd square matrix
 
     :rval L: the Cholesky decomposition of A
 
-    .. Note:
+    .. note:
+
       Adds jitter to K, to enforce positive-definiteness
       if stuff breaks, please check:
       np.allclose(sp.linalg.cholesky(XXT, lower = True), np.triu(sp.linalg.cho_factor(XXT)[0]).T)
+
     """
     try:
         return linalg.cholesky(A, lower=True)
@@ -150,6 +160,7 @@ def jitchol_old(A, maxtries=5):
 
 def pdinv(A, *args):
     """
+
     :param A: A DxD pd numpy array
 
     :rval Ai: the inverse of A
@@ -160,6 +171,7 @@ def pdinv(A, *args):
     :rtype Li: np.ndarray
     :rval logdet: the log of the determinant of A
     :rtype logdet: float64
+
     """
     L = jitchol(A, *args)
     logdet = 2.*np.sum(np.log(np.diag(L)))
@@ -185,14 +197,13 @@ def chol_inv(L):
 
 def multiple_pdinv(A):
     """
-    Arguments
-    ---------
     :param A: A DxDxN numpy array (each A[:,:,i] is pd)
 
-    Returns
+    :rval invs: the inverses of A
-    -------
+    :rtype invs: np.ndarray
-    invs : the inverses of A
+    :rval hld: 0.5* the log of the determinants of A
-    hld: 0.5* the log of the determinants of A
+    :rtype hld: np.array
+
     """
     N = A.shape[-1]
     chols = [jitchol(A[:, :, i]) for i in range(N)]
@@ -206,15 +217,13 @@ def PCA(Y, input_dim):
     """
     Principal component analysis: maximum likelihood solution by SVD
 
-    Arguments
-    ---------
     :param Y: NxD np.array of data
     :param input_dim: int, dimension of projection
 
-    Returns
+
-    -------
     :rval X: - Nxinput_dim np.array of dimensionality reduced data
-    W - input_dimxD mapping from X to Y
+    :rval W: - input_dimxD mapping from X to Y
+
     """
     if not np.allclose(Y.mean(axis=0), 0.0):
         print "Y is not zero mean, centering it locally (GPy.util.linalg.PCA)"
@@ -281,11 +290,10 @@ def DSYR_blas(A, x, alpha=1.):
     Performs a symmetric rank-1 update operation:
     A <- A + alpha * np.dot(x,x.T)
 
-    Arguments
-    ---------
     :param A: Symmetric NxN np.array
     :param x: Nx1 np.array
     :param alpha: scalar
+
     """
     N = c_int(A.shape[0])
     LDA = c_int(A.shape[0])
@@ -303,11 +311,10 @@ def DSYR_numpy(A, x, alpha=1.):
     Performs a symmetric rank-1 update operation:
     A <- A + alpha * np.dot(x,x.T)
 
-    Arguments
-    ---------
     :param A: Symmetric NxN np.array
     :param x: Nx1 np.array
     :param alpha: scalar
+
     """
     A += alpha * np.dot(x[:, None], x[None, :])
 
@@ -371,8 +378,9 @@ def cholupdate(L, x):
     """
     update the LOWER cholesky factor of a pd matrix IN PLACE
 
-    if L is the lower chol. of K, then this function computes L_
+    if L is the lower chol. of K, then this function computes L\_
-    where L_ is the lower chol of K + x*x^T
+    where L\_ is the lower chol of K + x*x^T
+
     """
     support_code = """
     #include <math.h>

GPy/util/ln_diff_erfs.py

@@ -0,0 +1,110 @@
+# Copyright (c) 2013, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+#Only works for scipy 0.12+
+try:
+    from scipy.special import erfcx, erf
+except ImportError:
+    from scipy.special import erf
+    from erfcx import erfcx
+
+import numpy as np
+
+def ln_diff_erfs(x1, x2, return_sign=False):
+    """Function for stably computing the log of difference of two erfs in a numerically stable manner.
+    :param x1 : argument of the positive erf
+    :type x1: ndarray
+    :param x2 : argument of the negative erf
+    :type x2: ndarray
+    :return: tuple containing (log(abs(erf(x1) - erf(x2))), sign(erf(x1) - erf(x2)))
+    
+    Based on MATLAB code that was written by Antti Honkela and modified by David Luengo and originally derived from code by Neil Lawrence.
+    """
+    x1 = np.require(x1).real
+    x2 = np.require(x2).real
+    if x1.size==1:
+        x1 = np.reshape(x1, (1, 1))
+    if x2.size==1:
+        x2 = np.reshape(x2, (1, 1))
+        
+    if x1.shape==x2.shape:
+        v = np.zeros_like(x1)
+    else:
+        if x1.size==1:
+            v = np.zeros(x2.shape)
+        elif x2.size==1:
+            v = np.zeros(x1.shape)
+        else:
+            raise ValueError, "This function does not broadcast unless provided with a scalar."
+    
+    if x1.size == 1:
+        x1 = np.tile(x1, x2.shape)
+
+    if x2.size == 1:
+        x2 = np.tile(x2, x1.shape)
+
+    sign = np.sign(x1 - x2)
+    if x1.size == 1:
+        if sign== -1:
+            swap = x1
+            x1 = x2
+            x2 = swap
+    else:
+        I = sign == -1
+        swap = x1[I]
+        x1[I] = x2[I]
+        x2[I] = swap
+
+    with np.errstate(divide='ignore'):
+        # switch off log of zero warnings.
+
+        # Case 0: arguments of different sign, no problems with loss of accuracy
+        I0 = np.logical_or(np.logical_and(x1>0, x2<0), np.logical_and(x2>0, x1<0)) # I1=(x1*x2)<0
+
+        # Case 1: x1 = x2 so we have log of zero.
+        I1 = (x1 == x2)
+
+        # Case 2: Both arguments are non-negative
+        I2 = np.logical_and(x1 > 0, np.logical_and(np.logical_not(I0),
+                                                   np.logical_not(I1)))
+        # Case 3: Both arguments are non-positive
+        I3 = np.logical_and(np.logical_and(np.logical_not(I0),
+                                           np.logical_not(I1)),
+                            np.logical_not(I2))
+        _x2 = x2.flatten()
+        _x1 = x1.flatten()
+        for group, flags in zip((0, 1, 2, 3), (I0, I1, I2, I3)):
+
+            if np.any(flags):
+                if not x1.size==1:
+                    _x1 = x1[flags]
+                if not x2.size==1:
+                    _x2 = x2[flags]
+                if group==0:
+                    v[flags] = np.log( erf(_x1) - erf(_x2) )
+                elif group==1:
+                    v[flags] = -np.inf
+                elif group==2:
+                    v[flags] = np.log(erfcx(_x2)
+                                   -erfcx(_x1)*np.exp(_x2**2
+                                                      -_x1**2)) - _x2**2
+                elif group==3:
+                    v[flags] = np.log(erfcx(-_x1)
+                                   -erfcx(-_x2)*np.exp(_x1**2
+                                                          -_x2**2))-_x1**2
+        
+    # TODO: switch back on log of zero warnings.
+
+    if return_sign:
+        return v, sign
+    else:
+        if v.size==1:
+            if sign==-1:
+                v = v.view('complex64')
+                v += np.pi*1j
+        else:
+            # Need to add in a complex part because argument is negative.
+            v = v.view('complex64')
+            v[I] += np.pi*1j
+
+    return v

GPy/util/misc.py

@@ -17,12 +17,9 @@ def linear_grid(D, n = 100, min_max = (-100, 100)):
     """
     Creates a D-dimensional grid of n linearly spaced points
 
-    Parameters:
+    :param D: dimension of the grid
-
+    :param n: number of points
-    D:        dimension of the grid
+    :param min_max: (min, max) list
-    n:        number of points
-    min_max:  (min, max) list
-
 
     """
 
@@ -39,6 +36,7 @@ def kmm_init(X, m = 10):
 
     :param X: data
     :param m: number of inducing points
+
     """
 
     # compute the distances

GPy/util/mocap.py

@@ -92,13 +92,15 @@ class tree:
 
 
     def swap_vertices(self, i, j):
-        """Swap two vertices in the tree structure array.
+        """
+        Swap two vertices in the tree structure array.
         swap_vertex swaps the location of two vertices in a tree structure array. 
-         ARG tree : the tree for which two vertices are to be swapped.
+
-         ARG i : the index of the first vertex to be swapped.
+        :param tree: the tree for which two vertices are to be swapped.
-         ARG j : the index of the second vertex to be swapped.
+        :param i: the index of the first vertex to be swapped.
-         RETURN tree : the tree structure with the two vertex locations
+        :param j: the index of the second vertex to be swapped.
-         swapped.
+        :rval tree: the tree structure with the two vertex locations swapped.
+
         """
         store_vertex_i = self.vertices[i]
         store_vertex_j = self.vertices[j]
@@ -117,12 +119,17 @@ class tree:
 
 def rotation_matrix(xangle, yangle, zangle, order='zxy', degrees=False):
 
-    """Compute the rotation matrix for an angle in each direction.
+    """
+
+    Compute the rotation matrix for an angle in each direction.
     This is a helper function for computing the rotation matrix for a given set of angles in a given order.
-     ARG xangle : rotation for x-axis.
+
-     ARG yangle : rotation for y-axis.
+    :param xangle: rotation for x-axis.
-     ARG zangle : rotation for z-axis.
+    :param yangle: rotation for y-axis.
-     ARG order : the order for the rotations."""
+    :param zangle: rotation for z-axis.
+    :param order: the order for the rotations.
+
+     """
     if degrees:
         xangle = math.radians(xangle)
         yangle = math.radians(yangle)
@@ -301,10 +308,12 @@ class acclaim_skeleton(skeleton):
 
     def load_skel(self, file_name):
 
-        """Loads an ASF file into a skeleton structure.
+        """
-        loads skeleton structure from an acclaim skeleton file.
+        Loads an ASF file into a skeleton structure.
-         ARG file_name : the file name to load in.
+
-         RETURN skel : the skeleton for the file."""         
+        :param file_name: The file name to load in.
+
+         """         
 
         fid = open(file_name, 'r')
         self.read_skel(fid)

GPy/util/multioutput.py

@@ -0,0 +1,35 @@
+import numpy as np
+import warnings
+from .. import kern
+
+def build_lcm(input_dim, num_outputs, CK = [], NC = [], W_columns=1,W=None,kappa=None):
+    #TODO build_icm or build_lcm
+    """
+    Builds a kernel for a linear coregionalization model
+
+    :input_dim: Input dimensionality
+    :num_outputs: Number of outputs
+    :param CK: List of coregionalized kernels (i.e., this will be multiplied by a coregionalize kernel).
+    :param K: List of kernels that will be added up together with CK, but won't be multiplied by a coregionalize kernel
+    :param W_columns: number tuples of the corregionalization parameters 'coregion_W'
+    :type W_columns: integer
+    """
+
+    for k in CK:
+        if k.input_dim <> input_dim:
+            k.input_dim = input_dim
+            warnings.warn("kernel's input dimension overwritten to fit input_dim parameter.")
+
+    for k in NC:
+        if k.input_dim <> input_dim + 1:
+            k.input_dim = input_dim + 1
+            warnings.warn("kernel's input dimension overwritten to fit input_dim parameter.")
+
+    kernel = CK[0].prod(kern.coregionalize(num_outputs,W_columns,W,kappa),tensor=True)
+    for k in CK[1:]:
+        k_coreg = kern.coregionalize(num_outputs,W_columns,W,kappa)
+        kernel += k.prod(k_coreg,tensor=True)
+    for k in NC:
+        kernel += k
+
+    return kernel

GPy/util/plot_latent.py

@@ -15,7 +15,7 @@ def most_significant_input_dimensions(model, which_indices):
             try:
                 input_1, input_2 = np.argsort(model.input_sensitivity())[::-1][:2]
             except:
-                raise ValueError, "cannot Atomatically determine which dimensions to plot, please pass 'which_indices'"
+                raise ValueError, "cannot automatically determine which dimensions to plot, please pass 'which_indices'"
     else:
         input_1, input_2 = which_indices
     return input_1, input_2

GPy/util/symbolic.py

@@ -0,0 +1,32 @@
+from sympy import Function, S, oo, I, cos, sin
+
+
+class sinc_grad(Function):
+    nargs = 1
+    
+    def fdiff(self, argindex=1):
+        return ((2-x*x)*sin(self.args[0]) - 2*x*cos(x))/(x*x*x)
+    
+    @classmethod
+    def eval(cls, x):
+        if x is S.Zero:
+            return S.Zero
+        else:
+            return (x*cos(x) - sin(x))/(x*x)
+            
+class sinc(Function):
+    
+    nargs = 1
+    
+    def fdiff(self, argindex=1):
+        return sinc_grad(self.args[0])
+    
+    @classmethod
+    def eval(cls, x):
+        if x is S.Zero:
+            return S.One
+        else:
+            return sin(x)/x
+    
+    def _eval_is_real(self):
+        return self.args[0].is_real

GPy/util/univariate_Gaussian.py

@@ -32,4 +32,15 @@ def std_norm_cdf(x):
     x = float(x)
     return weave.inline(code,arg_names=['x'],support_code=support_code)
 
+def inv_std_norm_cdf(x):
+    """
+    Inverse cumulative standard Gaussian distribution
+    Based on Winitzki, S. (2008)
+    """
+    z = 2*x -1
+    ln1z2 = np.log(1-z**2)
+    a = 8*(np.pi -3)/(3*np.pi*(4-np.pi))
+    b = 2/(np.pi * a) + ln1z2/2
+    inv_erf = np.sign(z) * np.sqrt( np.sqrt(b**2 - ln1z2/a) - b )
+    return np.sqrt(2) * inv_erf
 

GPy/util/visualize.py

@@ -502,11 +502,14 @@ def data_play(Y, visualizer, frame_rate=30):
 
     This example loads in the CMU mocap database (http://mocap.cs.cmu.edu) subject number 35 motion number 01. It then plays it using the mocap_show visualize object.
     
+    .. code-block:: python
+
        data = GPy.util.datasets.cmu_mocap(subject='35', train_motions=['01'])
        Y = data['Y']
        Y[:, 0:3] = 0.   # Make figure walk in place
        visualize = GPy.util.visualize.skeleton_show(Y[0, :], data['skel'])
        GPy.util.visualize.data_play(Y, visualize)
+
     """
     
 

GPy/util/warping_functions.py

@@ -53,9 +53,11 @@ class TanhWarpingFunction(WarpingFunction):
         self.num_parameters = 3 * self.n_terms
 
     def f(self,y,psi):
-        """transform y with f using parameter vector psi
+        """
+        transform y with f using parameter vector psi
         psi = [[a,b,c]]
-        f = \sum_{terms} a * tanh(b*(y+c))
+        ::math::`f = \\sum_{terms} a * tanh(b*(y+c))`
+
         """
 
         #1. check that number of params is consistent
@@ -77,8 +79,7 @@ class TanhWarpingFunction(WarpingFunction):
         """
         calculate the numerical inverse of f
 
-        == input ==
+        :param iterations: number of N.R. iterations
-        iterations: number of N.R. iterations
 
         """
 
@@ -165,9 +166,11 @@ class TanhWarpingFunction_d(WarpingFunction):
         self.num_parameters = 3 * self.n_terms + 1
 
     def f(self,y,psi):
-        """transform y with f using parameter vector psi
+        """
+        Transform y with f using parameter vector psi
         psi = [[a,b,c]]
-        f = \sum_{terms} a * tanh(b*(y+c))
+
+        :math:`f = \\sum_{terms} a * tanh(b*(y+c))`
         """
 
         #1. check that number of params is consistent
@@ -189,8 +192,7 @@ class TanhWarpingFunction_d(WarpingFunction):
         """
         calculate the numerical inverse of f
 
-        == input ==
+        :param max_iterations: maximum number of N.R. iterations
-        iterations: number of N.R. iterations
 
         """
 
@@ -214,12 +216,13 @@ class TanhWarpingFunction_d(WarpingFunction):
     def fgrad_y(self, y, psi, return_precalc = False):
         """
         gradient of f w.r.t to y ([N x 1])
-        returns: Nx1 vector of derivatives, unless return_precalc is true,
+
-        then it also returns the precomputed stuff
+        :returns: Nx1 vector of derivatives, unless return_precalc is true, then it also returns the precomputed stuff
+
         """
 
 
-        mpsi = psi.copy()
+        mpsi = psi.coSpy()
         d = psi[-1]
         mpsi = mpsi[:self.num_parameters-1].reshape(self.n_terms, 3)
 
@@ -242,7 +245,7 @@ class TanhWarpingFunction_d(WarpingFunction):
         """
         gradient of f w.r.t to y and psi
 
-        returns: NxIx4 tensor of partial derivatives
+        :returns: NxIx4 tensor of partial derivatives
 
         """
 

README.md

@@ -1,10 +1,57 @@
 GPy
 ===
 
-A Gaussian processes framework in python
+A Gaussian processes framework in Python.
 
 * [Online documentation](https://gpy.readthedocs.org/en/latest/)
 * [Unit tests (Travis-CI)](https://travis-ci.org/SheffieldML/GPy)
 
 
 Continuous integration status: ![CI status](https://travis-ci.org/SheffieldML/GPy.png)
+
+
+Compiling documentation:
+========================
+
+The documentation is stored in doc/ and is compiled with the Sphinx Python documentation generator, and is written in the reStructuredText format.
+
+The Sphinx documentation is available here: http://sphinx-doc.org/latest/contents.html
+
+
+Installing dependencies:
+------------------------
+
+To compile the documentation, first ensure that Sphinx is installed. On Debian-based systems, this can be achieved as follows:
+
+    sudo apt-get install python-pip
+    sudo pip install sphinx
+
+A LaTeX distribution is also required to compile the equations. Note that the extra packages are necessary to install the unicode packages. To compile the equations to PNG format for use in HTML pages, the package *dvipng* must be installed. IPython is also required. On Debian-based systems, this can be achieved as follows:
+
+    sudo apt-get install texlive texlive-latex-extra texlive-base texlive-recommended
+    sudo apt-get install dvipng
+    sudo apt-get install ipython
+
+
+Compiling documentation:
+------------------------
+
+The documentation can be compiled as follows:
+
+    cd doc
+    make html
+
+The HTML files are then stored in doc/_build/
+
+
+Running unit tests:
+===================
+
+Ensure nose is installed via pip:
+
+    pip install nose
+
+Run nosetests from the root directory of the repository:
+
+    nosetests -v
+

doc/GPy.core.rst

@@ -1,91 +1,102 @@
-core Package
+GPy.core package
-============
+================
 
-:mod:`core` Package
+Submodules
--------------------
+----------
 
-.. automodule:: GPy.core
+GPy.core.domains module
-    :members:
+-----------------------
-    :undoc-members:
-    :show-inheritance:
-
-:mod:`domains` Module
----------------------
 
 .. automodule:: GPy.core.domains
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`fitc` Module
+GPy.core.fitc module
-------------------
+--------------------
 
 .. automodule:: GPy.core.fitc
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`gp` Module
+GPy.core.gp module
-----------------
+------------------
 
 .. automodule:: GPy.core.gp
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`gp_base` Module
+GPy.core.gp_base module
----------------------
+-----------------------
 
 .. automodule:: GPy.core.gp_base
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`model` Module
+GPy.core.mapping module
--------------------
+-----------------------
+
+.. automodule:: GPy.core.mapping
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.core.model module
+---------------------
 
 .. automodule:: GPy.core.model
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`parameterized` Module
+GPy.core.parameterized module
----------------------------
+-----------------------------
 
 .. automodule:: GPy.core.parameterized
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`priors` Module
+GPy.core.priors module
---------------------
+----------------------
 
 .. automodule:: GPy.core.priors
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`sparse_gp` Module
+GPy.core.sparse_gp module
------------------------
+-------------------------
 
 .. automodule:: GPy.core.sparse_gp
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`svigp` Module
+GPy.core.svigp module
--------------------
+---------------------
 
 .. automodule:: GPy.core.svigp
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`transformations` Module
+GPy.core.transformations module
------------------------------
+-------------------------------
 
 .. automodule:: GPy.core.transformations
     :members:
     :undoc-members:
     :show-inheritance:
 
+
+Module contents
+---------------
+
+.. automodule:: GPy.core
+    :members:
+    :undoc-members:
+    :show-inheritance:

doc/GPy.examples.rst

@@ -1,51 +1,54 @@
-examples Package
+GPy.examples package
-================
+====================
 
-:mod:`examples` Package
+Submodules
------------------------
+----------
 
-.. automodule:: GPy.examples
+GPy.examples.classification module
-    :members:
+----------------------------------
-    :undoc-members:
-    :show-inheritance:
-
-:mod:`classification` Module
-----------------------------
 
 .. automodule:: GPy.examples.classification
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`dimensionality_reduction` Module
+GPy.examples.dimensionality_reduction module
---------------------------------------
+--------------------------------------------
 
 .. automodule:: GPy.examples.dimensionality_reduction
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`regression` Module
+GPy.examples.regression module
-------------------------
+------------------------------
 
 .. automodule:: GPy.examples.regression
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`stochastic` Module
+GPy.examples.stochastic module
-------------------------
+------------------------------
 
 .. automodule:: GPy.examples.stochastic
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`tutorials` Module
+GPy.examples.tutorials module
------------------------
+-----------------------------
 
 .. automodule:: GPy.examples.tutorials
     :members:
     :undoc-members:
     :show-inheritance:
 
+
+Module contents
+---------------
+
+.. automodule:: GPy.examples
+    :members:
+    :undoc-members:
+    :show-inheritance:

doc/GPy.inference.rst

@@ -1,51 +1,62 @@
-inference Package
+GPy.inference package
-=================
+=====================
 
-:mod:`conjugate_gradient_descent` Module
+Submodules
-----------------------------------------
+----------
+
+GPy.inference.conjugate_gradient_descent module
+-----------------------------------------------
 
 .. automodule:: GPy.inference.conjugate_gradient_descent
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`gradient_descent_update_rules` Module
+GPy.inference.gradient_descent_update_rules module
--------------------------------------------
+--------------------------------------------------
 
 .. automodule:: GPy.inference.gradient_descent_update_rules
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`optimization` Module
+GPy.inference.optimization module
---------------------------
+---------------------------------
 
 .. automodule:: GPy.inference.optimization
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`samplers` Module
+GPy.inference.samplers module
-----------------------
+-----------------------------
 
 .. automodule:: GPy.inference.samplers
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`scg` Module
+GPy.inference.scg module
------------------
+------------------------
 
 .. automodule:: GPy.inference.scg
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`sgd` Module
+GPy.inference.sgd module
------------------
+------------------------
 
 .. automodule:: GPy.inference.sgd
     :members:
     :undoc-members:
     :show-inheritance:
 
+
+Module contents
+---------------
+
+.. automodule:: GPy.inference
+    :members:
+    :undoc-members:
+    :show-inheritance:

doc/GPy.kern.parts.rst

@@ -0,0 +1,246 @@
+GPy.kern.parts package
+======================
+
+Submodules
+----------
+
+GPy.kern.parts.Brownian module
+------------------------------
+
+.. automodule:: GPy.kern.parts.Brownian
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.Matern32 module
+------------------------------
+
+.. automodule:: GPy.kern.parts.Matern32
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.Matern52 module
+------------------------------
+
+.. automodule:: GPy.kern.parts.Matern52
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.bias module
+--------------------------
+
+.. automodule:: GPy.kern.parts.bias
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.coregionalize module
+-----------------------------------
+
+.. automodule:: GPy.kern.parts.coregionalize
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.exponential module
+---------------------------------
+
+.. automodule:: GPy.kern.parts.exponential
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.finite_dimensional module
+----------------------------------------
+
+.. automodule:: GPy.kern.parts.finite_dimensional
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.fixed module
+---------------------------
+
+.. automodule:: GPy.kern.parts.fixed
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.gibbs module
+---------------------------
+
+.. automodule:: GPy.kern.parts.gibbs
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.hetero module
+----------------------------
+
+.. automodule:: GPy.kern.parts.hetero
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.hierarchical module
+----------------------------------
+
+.. automodule:: GPy.kern.parts.hierarchical
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.independent_outputs module
+-----------------------------------------
+
+.. automodule:: GPy.kern.parts.independent_outputs
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.kernpart module
+------------------------------
+
+.. automodule:: GPy.kern.parts.kernpart
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.linear module
+----------------------------
+
+.. automodule:: GPy.kern.parts.linear
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.mlp module
+-------------------------
+
+.. automodule:: GPy.kern.parts.mlp
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.periodic_Matern32 module
+---------------------------------------
+
+.. automodule:: GPy.kern.parts.periodic_Matern32
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.periodic_Matern52 module
+---------------------------------------
+
+.. automodule:: GPy.kern.parts.periodic_Matern52
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.periodic_exponential module
+------------------------------------------
+
+.. automodule:: GPy.kern.parts.periodic_exponential
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.poly module
+--------------------------
+
+.. automodule:: GPy.kern.parts.poly
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.prod module
+--------------------------
+
+.. automodule:: GPy.kern.parts.prod
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.prod_orthogonal module
+-------------------------------------
+
+.. automodule:: GPy.kern.parts.prod_orthogonal
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.rational_quadratic module
+----------------------------------------
+
+.. automodule:: GPy.kern.parts.rational_quadratic
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.rbf module
+-------------------------
+
+.. automodule:: GPy.kern.parts.rbf
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.rbf_inv module
+-----------------------------
+
+.. automodule:: GPy.kern.parts.rbf_inv
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.rbfcos module
+----------------------------
+
+.. automodule:: GPy.kern.parts.rbfcos
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.spline module
+----------------------------
+
+.. automodule:: GPy.kern.parts.spline
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.symmetric module
+-------------------------------
+
+.. automodule:: GPy.kern.parts.symmetric
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.sympykern module
+-------------------------------
+
+.. automodule:: GPy.kern.parts.sympykern
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.parts.white module
+---------------------------
+
+.. automodule:: GPy.kern.parts.white
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+
+Module contents
+---------------
+
+.. automodule:: GPy.kern.parts
+    :members:
+    :undoc-members:
+    :show-inheritance:

doc/GPy.kern.rst

@@ -1,29 +1,5 @@
-kern Package
+GPy.kern package
-============
+================
-
-:mod:`kern` Package
--------------------
-
-.. automodule:: GPy.kern
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-:mod:`constructors` Module
---------------------------
-
-.. automodule:: GPy.kern.constructors
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-:mod:`kern` Module
-------------------
-
-.. automodule:: GPy.kern.kern
-    :members:
-    :undoc-members:
-    :show-inheritance:
 
 Subpackages
 -----------
@@ -32,3 +8,30 @@ Subpackages
 
     GPy.kern.parts
 
+Submodules
+----------
+
+GPy.kern.constructors module
+----------------------------
+
+.. automodule:: GPy.kern.constructors
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.kern.kern module
+--------------------
+
+.. automodule:: GPy.kern.kern
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+
+Module contents
+---------------
+
+.. automodule:: GPy.kern
+    :members:
+    :undoc-members:
+    :show-inheritance:

doc/GPy.likelihoods.noise_models.rst

@@ -0,0 +1,70 @@
+GPy.likelihoods.noise_models package
+====================================
+
+Submodules
+----------
+
+GPy.likelihoods.noise_models.binomial_noise module
+--------------------------------------------------
+
+.. automodule:: GPy.likelihoods.noise_models.binomial_noise
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.likelihoods.noise_models.exponential_noise module
+-----------------------------------------------------
+
+.. automodule:: GPy.likelihoods.noise_models.exponential_noise
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.likelihoods.noise_models.gamma_noise module
+-----------------------------------------------
+
+.. automodule:: GPy.likelihoods.noise_models.gamma_noise
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.likelihoods.noise_models.gaussian_noise module
+--------------------------------------------------
+
+.. automodule:: GPy.likelihoods.noise_models.gaussian_noise
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.likelihoods.noise_models.gp_transformations module
+------------------------------------------------------
+
+.. automodule:: GPy.likelihoods.noise_models.gp_transformations
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.likelihoods.noise_models.noise_distributions module
+-------------------------------------------------------
+
+.. automodule:: GPy.likelihoods.noise_models.noise_distributions
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.likelihoods.noise_models.poisson_noise module
+-------------------------------------------------
+
+.. automodule:: GPy.likelihoods.noise_models.poisson_noise
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+
+Module contents
+---------------
+
+.. automodule:: GPy.likelihoods.noise_models
+    :members:
+    :undoc-members:
+    :show-inheritance:

doc/GPy.likelihoods.rst

@@ -1,51 +1,69 @@
-likelihoods Package
+GPy.likelihoods package
-===================
+=======================
 
-:mod:`likelihoods` Package
+Subpackages
---------------------------
+-----------
 
-.. automodule:: GPy.likelihoods
+.. toctree::
-    :members:
-    :undoc-members:
-    :show-inheritance:
 
-:mod:`ep` Module
+    GPy.likelihoods.noise_models
-----------------
+
+Submodules
+----------
+
+GPy.likelihoods.ep module
+-------------------------
 
 .. automodule:: GPy.likelihoods.ep
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`gaussian` Module
+GPy.likelihoods.ep_mixed_noise module
-----------------------
+-------------------------------------
+
+.. automodule:: GPy.likelihoods.ep_mixed_noise
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.likelihoods.gaussian module
+-------------------------------
 
 .. automodule:: GPy.likelihoods.gaussian
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`likelihood` Module
+GPy.likelihoods.gaussian_mixed_noise module
-------------------------
+-------------------------------------------
+
+.. automodule:: GPy.likelihoods.gaussian_mixed_noise
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.likelihoods.likelihood module
+---------------------------------
 
 .. automodule:: GPy.likelihoods.likelihood
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`likelihood_functions` Module
+GPy.likelihoods.noise_model_constructors module
-----------------------------------
+-----------------------------------------------
 
-.. automodule:: GPy.likelihoods.likelihood_functions
+.. automodule:: GPy.likelihoods.noise_model_constructors
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`link_functions` Module
-----------------------------
 
-.. automodule:: GPy.likelihoods.link_functions
+Module contents
+---------------
+
+.. automodule:: GPy.likelihoods
     :members:
     :undoc-members:
     :show-inheritance:
-

doc/GPy.mappings.rst

@@ -0,0 +1,38 @@
+GPy.mappings package
+====================
+
+Submodules
+----------
+
+GPy.mappings.kernel module
+--------------------------
+
+.. automodule:: GPy.mappings.kernel
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.mappings.linear module
+--------------------------
+
+.. automodule:: GPy.mappings.linear
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.mappings.mlp module
+-----------------------
+
+.. automodule:: GPy.mappings.mlp
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+
+Module contents
+---------------
+
+.. automodule:: GPy.mappings
+    :members:
+    :undoc-members:
+    :show-inheritance:

doc/GPy.models.rst

@@ -1,99 +1,134 @@
-models Package
+GPy.models package
-==============
+==================
 
-:mod:`models` Package
+Submodules
----------------------
+----------
 
-.. automodule:: GPy.models
+GPy.models.bayesian_gplvm module
-    :members:
+--------------------------------
-    :undoc-members:
-    :show-inheritance:
-
-:mod:`bayesian_gplvm` Module
-----------------------------
 
 .. automodule:: GPy.models.bayesian_gplvm
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`fitc_classification` Module
+GPy.models.bcgplvm module
----------------------------------
+-------------------------
+
+.. automodule:: GPy.models.bcgplvm
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.models.fitc_classification module
+-------------------------------------
 
 .. automodule:: GPy.models.fitc_classification
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`gp_classification` Module
+GPy.models.gp_classification module
--------------------------------
+-----------------------------------
 
 .. automodule:: GPy.models.gp_classification
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`gp_regression` Module
+GPy.models.gp_multioutput_regression module
----------------------------
+-------------------------------------------
+
+.. automodule:: GPy.models.gp_multioutput_regression
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.models.gp_regression module
+-------------------------------
 
 .. automodule:: GPy.models.gp_regression
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`gplvm` Module
+GPy.models.gplvm module
--------------------
+-----------------------
 
 .. automodule:: GPy.models.gplvm
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`mrd` Module
+GPy.models.gradient_checker module
------------------
+----------------------------------
+
+.. automodule:: GPy.models.gradient_checker
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.models.mrd module
+---------------------
 
 .. automodule:: GPy.models.mrd
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`sparse_gp_classification` Module
+GPy.models.sparse_gp_classification module
---------------------------------------
+------------------------------------------
 
 .. automodule:: GPy.models.sparse_gp_classification
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`sparse_gp_regression` Module
+GPy.models.sparse_gp_multioutput_regression module
-----------------------------------
+--------------------------------------------------
+
+.. automodule:: GPy.models.sparse_gp_multioutput_regression
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.models.sparse_gp_regression module
+--------------------------------------
 
 .. automodule:: GPy.models.sparse_gp_regression
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`sparse_gplvm` Module
+GPy.models.sparse_gplvm module
---------------------------
+------------------------------
 
 .. automodule:: GPy.models.sparse_gplvm
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`svigp_regression` Module
+GPy.models.svigp_regression module
-------------------------------
+----------------------------------
 
 .. automodule:: GPy.models.svigp_regression
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`warped_gp` Module
+GPy.models.warped_gp module
------------------------
+---------------------------
 
 .. automodule:: GPy.models.warped_gp
     :members:
     :undoc-members:
     :show-inheritance:
 
+
+Module contents
+---------------
+
+.. automodule:: GPy.models
+    :members:
+    :undoc-members:
+    :show-inheritance:

doc/GPy.rst

@@ -1,14 +1,6 @@
-GPy Package
+GPy package
 ===========
 
-:mod:`GPy` Package
-------------------
-
-.. automodule:: GPy.__init__
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
 Subpackages
 -----------
 
@@ -19,7 +11,15 @@ Subpackages
     GPy.inference
     GPy.kern
     GPy.likelihoods
+    GPy.mappings
     GPy.models
     GPy.testing
     GPy.util
 
+Module contents
+---------------
+
+.. automodule:: GPy
+    :members:
+    :undoc-members:
+    :show-inheritance:

doc/GPy.testing.rst

@@ -1,107 +1,110 @@
-testing Package
+GPy.testing package
-===============
+===================
 
-:mod:`testing` Package
+Submodules
-----------------------
+----------
 
-.. automodule:: GPy.testing
+GPy.testing.bgplvm_tests module
-    :members:
+-------------------------------
-    :undoc-members:
-    :show-inheritance:
-
-:mod:`bgplvm_tests` Module
---------------------------
 
 .. automodule:: GPy.testing.bgplvm_tests
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`cgd_tests` Module
+GPy.testing.cgd_tests module
------------------------
+----------------------------
 
 .. automodule:: GPy.testing.cgd_tests
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`checkgrad` Module
+GPy.testing.examples_tests module
------------------------
+---------------------------------
-
-.. automodule:: GPy.testing.checkgrad
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-:mod:`examples_tests` Module
-----------------------------
 
 .. automodule:: GPy.testing.examples_tests
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`gplvm_tests` Module
+GPy.testing.gplvm_tests module
--------------------------
+------------------------------
 
 .. automodule:: GPy.testing.gplvm_tests
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`kernel_tests` Module
+GPy.testing.kernel_tests module
---------------------------
+-------------------------------
 
 .. automodule:: GPy.testing.kernel_tests
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`mrd_tests` Module
+GPy.testing.mapping_tests module
------------------------
+--------------------------------
+
+.. automodule:: GPy.testing.mapping_tests
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.testing.mrd_tests module
+----------------------------
 
 .. automodule:: GPy.testing.mrd_tests
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`prior_tests` Module
+GPy.testing.prior_tests module
--------------------------
+------------------------------
 
 .. automodule:: GPy.testing.prior_tests
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`psi_stat_expactation_tests` Module
+GPy.testing.psi_stat_expectation_tests module
-----------------------------------------
+---------------------------------------------
 
-.. automodule:: GPy.testing.psi_stat_expactation_tests
+.. automodule:: GPy.testing.psi_stat_expectation_tests
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`psi_stat_gradient_tests` Module
+GPy.testing.psi_stat_gradient_tests module
--------------------------------------
+------------------------------------------
 
 .. automodule:: GPy.testing.psi_stat_gradient_tests
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`sparse_gplvm_tests` Module
+GPy.testing.sparse_gplvm_tests module
---------------------------------
+-------------------------------------
 
 .. automodule:: GPy.testing.sparse_gplvm_tests
     :members:
     :undoc-members:
     :show-inheritance:
 
-:mod:`unit_tests` Module
+GPy.testing.unit_tests module
-------------------------
+-----------------------------
 
 .. automodule:: GPy.testing.unit_tests
     :members:
     :undoc-members:
     :show-inheritance:
 
+
+Module contents
+---------------
+
+.. automodule:: GPy.testing
+    :members:
+    :undoc-members:
+    :show-inheritance:

doc/GPy.util.latent_space_visualizations.controllers.rst

@@ -0,0 +1,30 @@
+GPy.util.latent_space_visualizations.controllers package
+========================================================
+
+Submodules
+----------
+
+GPy.util.latent_space_visualizations.controllers.axis_event_controller module
+-----------------------------------------------------------------------------
+
+.. automodule:: GPy.util.latent_space_visualizations.controllers.axis_event_controller
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+GPy.util.latent_space_visualizations.controllers.imshow_controller module
+-------------------------------------------------------------------------
+
+.. automodule:: GPy.util.latent_space_visualizations.controllers.imshow_controller
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+
+Module contents
+---------------
+
+.. automodule:: GPy.util.latent_space_visualizations.controllers
+    :members:
+    :undoc-members:
+    :show-inheritance: