tidied up gp_base and gp

GPy/core/gp.py

@@ -1,10 +1,7 @@
 # Copyright (c) 2012, GPy authors (see AUTHORS.txt).
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
-
 import numpy as np
-from ..util.linalg import pdinv, tdot, dpotrs, dtrtrs
-from ..likelihoods import EP
 from gp_base import GPBase
 
 class GP(GPBase):
@@ -23,104 +20,36 @@ class GP(GPBase):
     """
     def __init__(self, X, likelihood, kernel, normalize_X=False):
         super(GP, self).__init__(X, likelihood, kernel, normalize_X=normalize_X)
-        #self._set_params(self._get_params())
+        self.Posterior = self.inference_method.inference(K, likelihood, self.Y)
-
-    def getstate(self):
-        return GPBase.getstate(self)
-
-    def setstate(self, state):
-        GPBase.setstate(self, state)
-        #self._set_params(self._get_params())
 
     def parameters_changed(self):
         super(GP, self).parameters_changed()
         self.K = self.kern.K(self.X)
-        self.K += self.likelihood.covariance_matrix
+        self.Posterior = self.inference_method.inference(K, likelihood, self.Y)
-        self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K)
-
-        # the gradient of the likelihood wrt the covariance matrix
-        if self.likelihood.YYT is None:
-            # alpha = np.dot(self.Ki, self.likelihood.Y)
-            alpha, _ = dpotrs(self.L, self.likelihood.Y, lower=1)
-
-            self.dL_dK = 0.5 * (tdot(alpha) - self.output_dim * self.Ki)
-        else:
-            # tmp = mdot(self.Ki, self.likelihood.YYT, self.Ki)
-            tmp, _ = dpotrs(self.L, np.asfortranarray(self.likelihood.YYT), lower=1)
-            tmp, _ = dpotrs(self.L, np.asfortranarray(tmp.T), lower=1)
-            self.dL_dK = 0.5 * (tmp - self.output_dim * self.Ki)
-
-#     def _get_params(self):
-#         return np.hstack((self.kern._get_params_transformed(), self.likelihood._get_params()))
-
-#     def _get_param_names(self):
-#         return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
-
-    def update_likelihood_approximation(self, **kwargs):
-        """
-        Approximates a non-gaussian likelihood using Expectation Propagation
-
-        For a Gaussian likelihood, no iteration is required:
-        this function does nothing
-        """
-        self.likelihood.restart()
-        self.likelihood.fit_full(self.kern.K(self.X), **kwargs)
-#         self._set_params(self._get_params()) # update the GP
-
-    def _model_fit_term(self):
-        """
-        Computes the model fit using YYT if it's available
-        """
-        if self.likelihood.YYT is None:
-            tmp, _ = dtrtrs(self.L, np.asfortranarray(self.likelihood.Y), lower=1)
-            return -0.5 * np.sum(np.square(tmp))
-            # return -0.5 * np.sum(np.square(np.dot(self.Li, self.likelihood.Y)))
-        else:
-            return -0.5 * np.sum(np.multiply(self.Ki, self.likelihood.YYT))
 
     def log_likelihood(self):
-        """
+        return self.posterior.log_marginal
-        The log marginal likelihood of the GP.
-
-        For an EP model,  can be written as the log likelihood of a regression
-        model for a new variable Y* = v_tilde/tau_tilde, with a covariance
-        matrix K* = K + diag(1./tau_tilde) plus a normalization term.
-        """
-        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
-#         """
-#         #return np.hstack((self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X), self.likelihood._gradients(partial=np.diag(self.dL_dK))))
-#         
-#         if not isinstance(self.likelihood,EP):
-#             tmp = np.hstack((self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X), self.likelihood._gradients(partial=np.diag(self.dL_dK))))
-#         else:
-#             tmp = np.hstack((self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X), self.likelihood._gradients(partial=np.diag(self.dL_dK))))
-#         return tmp
 
     def _raw_predict(self, _Xnew, which_parts='all', full_cov=False, stop=False):
         """
         Internal helper function for making predictions, does not account
         for normalization or likelihood
+
+        full_cov is a boolean which defines whether the full covariance matrix
+        of the prediction is computed. If full_cov is False (default), only the
+        diagonal of the covariance is returned.
+
         """
         Kx = self.kern.K(_Xnew, self.X, which_parts=which_parts).T
-        # KiKx = np.dot(self.Ki, Kx)
+        LiKx, _ = dptrrs(self.posterior._woodbury_chol, np.asfortranarray(Kx), lower=1)
-        KiKx, _ = dpotrs(self.L, np.asfortranarray(Kx), lower=1)
+        mu = np.dot(Kx.T, self.posterior._woodbury_vector)
-        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)
+            var = Kxx - tdot(LiKx.T)
         else:
             Kxx = self.kern.Kdiag(_Xnew, which_parts=which_parts)
-            var = Kxx - np.sum(np.multiply(KiKx, Kx), 0)
+            var = Kxx - np.sum(LiKx.T*LiKx, 0)
-            var = var[:, None]
+            var = var.reshape(self.num_data, 1)
-        if stop:
-            debug_this # @UndefinedVariable
         return mu, var
 
     def predict(self, Xnew, which_parts='all', full_cov=False, **likelihood_args):
@@ -150,41 +79,4 @@ class GP(GPBase):
         mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov, **likelihood_args)
         return mean, var, _025pm, _975pm
 
-    def _raw_predict_single_output(self, _Xnew, output, which_parts='all', full_cov=False,stop=False):
-        """
-        For a specific output, calls _raw_predict() at the new point(s) _Xnew.
-        This functions calls _add_output_index(), so _Xnew should not have an index column specifying the output.
-        ---------
 
-        :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,..., output_dim-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 non-independent outputs models only.
-        """
-        _Xnew = self._add_output_index(_Xnew, output)
-        return self._raw_predict(_Xnew, which_parts=which_parts,full_cov=full_cov, stop=stop)
-
-    def predict_single_output(self, Xnew,output=0, which_parts='all', full_cov=False, likelihood_args=dict()):
-        """
-        For a specific output, calls predict() at the new point(s) Xnew.
-        This functions calls _add_output_index(), so Xnew should not have an index column specifying the output.
-
-        :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 full covariance matrix, or just the diagonal
-        :type full_cov: bool
-        :returns: mean: posterior mean,  a Numpy array, Nnew x self.input_dim
-        :returns: var: 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 non-independent outputs models only.
-        """
-        Xnew = self._add_output_index(Xnew, output)
-        return self.predict(Xnew, which_parts=which_parts, full_cov=full_cov, likelihood_args=likelihood_args)

GPy/core/gp_base.py

@@ -1,10 +1,9 @@
 import numpy as np
+import pylab as pb
+import warnings
 from .. import kern
 from ..util.plot import gpplot, Tango, x_frame1D, x_frame2D
-import pylab as pb
 from model import Model
-import warnings
-from ..likelihoods import Gaussian, Gaussian_Mixed_Noise
 from ..core.parameter import ObservableArray
 
 class GPBase(Model):
@@ -12,17 +11,27 @@ class GPBase(Model):
     Gaussian process base model for holding shared behaviour between
     sparse_GP and GP models.
     """
-    def __init__(self, X, likelihood, kernel, normalize_X=False, name=''):
+    def __init__(self, X, Y, kernel, normalize_X=False, inference_method=None, name=''):
         super(GPBase, self).__init__(name)
         
+        assert X.ndim == 2
         self.X = ObservableArray(X)
-        assert len(self.X.shape) == 2
         self.num_data, self.input_dim = self.X.shape
+
         assert isinstance(kernel, kern.kern)
         self.kern = kernel
+
+        assert isinstance(likelihood, likelihoods.Likelihood)
         self.likelihood = likelihood
-        assert self.X.shape[0] == self.likelihood.data.shape[0]
+
-        self.num_data, self.output_dim = self.likelihood.data.shape
+        if inference_method is None:
+            self.inference_method = self.likelihood.preferred_inference_method
+            print "defaulting to ", inference_method, "for latent function inference"
+        else:
+            self.inference_method = inference_method
+
+        assert self.X.shape[0] == Y.shape[0]
+        self.num_data, self.output_dim = self.Y.shape
 
         if normalize_X:
             self._Xoffset = X.mean(0)[None, :]
@@ -34,40 +43,6 @@ class GPBase(Model):
         
         self.add_parameter(self.kern, gradient=lambda:self.kern.dK_dtheta(self.dL_dK, self.X))
         self.add_parameter(self.likelihood, gradient=lambda:self.likelihood._gradients(partial=np.diag(self.dL_dK)))
-        #self.kern.connect_input(self.X)
-        
-        # Model.__init__(self)
-        # All leaf nodes should call self._set_params(self._get_params()) at
-        # the end
-# 
-#     def parameters_changed(self):
-#         self.kern.parameters_changed()
-#         self.likelihood.parameters_changed()
-
-    def getstate(self):
-        """
-        Get the current state of the class, here we return everything that is needed to recompute the model.
-        """
-        return Model.getstate(self) + [self.X,
-                self.num_data,
-                self.input_dim,
-                self.kern,
-                self.likelihood,
-                self.output_dim,
-                self._Xoffset,
-                self._Xscale,
-                ]
-
-    def setstate(self, state):
-        self._Xscale = state.pop()
-        self._Xoffset = state.pop()
-        self.output_dim = state.pop()
-        self.likelihood = state.pop()
-        self.kern = state.pop()
-        self.input_dim = state.pop()
-        self.num_data = state.pop()
-        self.X = state.pop()
-        Model.setstate(self, state)
 
     def posterior_samples_f(self,X,size=10,which_parts='all',full_cov=True):
         """
@@ -121,90 +96,43 @@ class GPBase(Model):
 
         return Ysim
 
-    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, *args, **kwargs):
         """
-        Plot the GP's view of the world, where the data is normalized and the
+        Plot the GP's view of the world, where the data is normalized and before applying a likelihood.
-          - 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
-          - Not implemented in higher dimensions
 
-        :param samples: the number of a posteriori samples to plot
+        This is a convenience function: we simply call self.plot with the
-        :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
+        argument use_raw_predict set True. All args and kwargs are passed on to
-        :param which_data: which if the training data to plot (default all)
+        plot.
-        :type which_data: 'all' or a slice object to slice self.X, self.Y
-        :param which_parts: which of the kernel functions to plot (additively)
-        :type which_parts: 'all', or list of bools
-        :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
-        :type resolution: int
-        :param full_cov:
-        :type full_cov: bool
-                :param fignum: figure to plot on.
-        :type fignum: figure number
-        :param ax: axes to plot on.
-        :type ax: axes handle
 
-        :param output: which output to plot (for multiple output models only)
+        see also: gp_base.plot
-        :type output: integer (first output is 0)
         """
-        if which_data == 'all':
+        kwargs['plot_raw'] = True
-            which_data = slice(None)
+        self.plot(*args, **kwargs)
 
-        if ax is None:
+    def plot(self, plot_limits=None, which_data_rows='all',
-            fig = pb.figure(num=fignum)
+            which_data_ycols='all', which_parts='all', fixed_inputs=[],
-            ax = fig.add_subplot(111)
+            levels=20, samples=0, fignum=None, ax=None, resolution=None,
-
+            plot_raw=False,
-        if self.X.shape[1] == 1:
+            linecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue']):
-            resolution = resolution or 200
-            Xnew, xmin, xmax = x_frame1D(self.X, plot_limits=plot_limits)
-
-            m, v = self._raw_predict(Xnew, which_parts=which_parts)
-            if samples:
-                Ysim = self.posterior_samples_f(Xnew, samples, which_parts=which_parts, full_cov=True)
-                for yi in Ysim.T:
-                    ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25)
-            gpplot(Xnew, m, m - 2 * np.sqrt(v), m + 2 * np.sqrt(v), axes=ax)
-
-            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)
-
-        elif self.X.shape[1] == 2:
-
-            resolution = resolution or 50
-            Xnew, xmin, xmax, xx, yy = x_frame2D(self.X, plot_limits, resolution)
-            m, v = self._raw_predict(Xnew, which_parts=which_parts)
-            m = m.reshape(resolution, resolution).T
-            ax.contour(xx, yy, m, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) # @UndefinedVariable
-            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])
-
-            if samples:
-                warnings.warn("Samples only implemented for 1 dimensional inputs.")
-
-        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']):
         """
-        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
-          - Not implemented in higher dimensions
+          - In higher dimensions, use fixed_inputs to plot the GP  with some of the inputs fixed.
 
         Can plot only part of the data and part of the posterior functions
-        using which_data and which_functions
+        using which_data_rowsm which_data_ycols and which_parts
 
         :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
         :type plot_limits: np.array
-        :param which_data: which if the training data to plot (default all)
+        :param which_data_rows: which of the training data to plot (default all)
-        :type which_data: 'all' or a slice object to slice self.X, self.Y
+        :type which_data_rows: 'all' or a slice object to slice self.X, self.Y
+        :param which_data_ycols: when the data has several columns (independant outputs), only plot these
+        :type which_data_rows: 'all' or a list of integers
         :param which_parts: which of the kernel functions to plot (additively)
         :type which_parts: 'all', or list of bools
+        :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 resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
         :type resolution: int
         :param levels: number of levels to plot in a contour plot.
@@ -216,216 +144,125 @@ class GPBase(Model):
         :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
         :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
         """
-        if which_data == 'all':
+        #deal with optional arguments
-            which_data = slice(None)
+        if which_data_rows == 'all':
-
+            which_data_rows = slice(None)
+        if which_data_ycols == 'all':
+            which_data_ycols = np.arange(self.output_dim)
+        if len(which_data_ycols)==0:
+            raise ValueError('No data selected for plotting')
         if ax is None:
             fig = pb.figure(num=fignum)
             ax = fig.add_subplot(111)
 
-        plotdims = self.input_dim - len(fixed_inputs)
+        #work out what the inputs are for plotting (1D or 2D)
-        if plotdims == 1:
+        fixed_dims = np.array([i for i,v in fixed_inputs])
+        free_dims = np.setdiff1d(np.arange(self.input_dim),fixed_dims)
+
+        #one dimensional plotting
+        if len(free_dims) == 1:
+
+            #define the frame on which to plot
             resolution = resolution or 200
-
             Xu = self.X * self._Xscale + self._Xoffset #NOTE self.X are the normalized values now
-
+            Xnew, xmin, xmax = x_frame1D(Xu[:,free_dims], plot_limits=plot_limits)
-            fixed_dims = np.array([i for i,v in fixed_inputs])
-            freedim = np.setdiff1d(np.arange(self.input_dim),fixed_dims)
-
-            Xnew, xmin, xmax = x_frame1D(Xu[:,freedim], plot_limits=plot_limits)
             Xgrid = np.empty((Xnew.shape[0],self.input_dim))
-            Xgrid[:,freedim] = Xnew
+            Xgrid[:,free_dims] = Xnew
             for i,v in fixed_inputs:
                 Xgrid[:,i] = v
 
-            m, v, lower, upper = self.predict(Xgrid, which_parts=which_parts)
+            #make a prediction on the frame and plot it
+            if plot_raw:
+                m, v = self._raw_predict(Xgrid, which_parts=which_parts)
+                lower = m - 2*np.sqrt(v)
+                upper = m + 2*np.sqrt(v)
+                Y = self.likelihood.Y
+            else:
+                m, v, lower, upper = self.predict(Xgrid, which_parts=which_parts, sampling=False) #Compute the exact mean
+                m_, v_, lower, upper = self.predict(Xgrid, which_parts=which_parts, sampling=True, num_samples=15000) #Apporximate the percentiles
+                Y = self.likelihood.data
+            for d in which_data_ycols:
+                gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax, edgecol=linecol, fillcol=fillcol)
+                ax.plot(Xu[which_data_rows,free_dims], Y[which_data_rows, d], 'kx', mew=1.5)
 
+            #optionally plot some samples
             if samples: #NOTE not tested with fixed_inputs
-                Ysim = self.posterior_samples(Xgrid, samples, which_parts=which_parts, full_cov=True)
+                Ysim = self.posterior_samples(Xgrid, samples, which_parts=which_parts)
                 for yi in Ysim.T:
                     ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25)
                     #ax.plot(Xnew, yi[:,None], marker='x', linestyle='--',color=Tango.colorsHex['darkBlue']) #TODO apply this line for discrete outputs.
 
-            for d in range(m.shape[1]):
+            #set the limits of the plot to some sensible values
-                gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax, edgecol=linecol, fillcol=fillcol)
+            ymin, ymax = min(np.append(Y[which_data_rows, which_data_ycols].flatten(), lower)), max(np.append(Y[which_data_rows, which_data_ycols].flatten(), upper))
-                ax.plot(Xu[which_data,freedim], 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:
+        #2D plotting
+        elif len(free_dims) == 2:
 
+            #define the frame for plotting on
             resolution = resolution or 50
-            Xnew, _, _, xmin, xmax = x_frame2D(self.X, plot_limits, resolution)
+            Xu = self.X * self._Xscale + self._Xoffset #NOTE self.X are the normalized values now
+            Xnew, _, _, xmin, xmax = x_frame2D(Xu[:,free_dims], plot_limits, resolution)
+            Xgrid = np.empty((Xnew.shape[0],self.input_dim))
+            Xgrid[:,free_dims] = Xnew
+            for i,v in fixed_inputs:
+                Xgrid[:,i] = v
             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
+            #predict on the frame and plot
-            ax.contour(x, y, m, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) # @UndefinedVariable
+            if plot_raw:
-            Yf = self.likelihood.Y.flatten()
+                m, _ = self._raw_predict(Xgrid, which_parts=which_parts)
-            ax.scatter(self.X[:, 0], self.X[:, 1], 40, Yf, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.) # @UndefinedVariable
+                Y = self.likelihood.Y
+            else:
+                m, _, _, _ = self.predict(Xgrid, which_parts=which_parts,sampling=False)
+                Y = self.likelihood.data
+            for d in which_data_ycols:
+                m_d = m[:,d].reshape(resolution, resolution).T
+                ax.contour(x, y, m_d, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet)
+                ax.scatter(self.X[which_data_rows, free_dims[0]], self.X[which_data_rows, free_dims[1]], 40, Y[which_data_rows, d], cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.)
+
+            #set the limits of the plot to some sensible values
             ax.set_xlim(xmin[0], xmax[0])
             ax.set_ylim(xmin[1], xmax[1])
 
             if samples:
-                warnings.warn("Samples only implemented for 1 dimensional inputs.")
+                warnings.warn("Samples are rather difficult to plot for 2D inputs...")
-
-        else:
-            raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
-
-    def plot_single_output_f(self, output=None, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, full_cov=False, fignum=None, ax=None):
-        """
-        For a specific output, in a multioutput model, this function works just as plot_f on single output models.
-
-        :param output: which output to plot (for multiple output models only)
-        :type output: integer (first output is 0)
-        :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
-        :param which_data: which if the training data to plot (default all)
-        :type which_data: 'all' or a slice object to slice self.X, self.Y
-        :param which_parts: which of the kernel functions to plot (additively)
-        :type which_parts: 'all', or list of bools
-        :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
-        :type resolution: int
-        :param full_cov:
-        :type full_cov: bool
-                :param fignum: figure to plot on.
-        :type fignum: figure number
-        :param ax: axes to plot on.
-        :type ax: axes handle
-        """
-        assert output is not None, "An output must be specified."
-        assert len(self.likelihood.noise_model_list) > output, "The model has only %s outputs." %(self.output_dim + 1)
-
-        if which_data == 'all':
-            which_data = slice(None)
-
-        if ax is None:
-            fig = pb.figure(num=fignum)
-            ax = fig.add_subplot(111)
-
-        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)
-            Xnew_indexed = self._add_output_index(Xnew,output)
-
-            m, v = self._raw_predict(Xnew_indexed, which_parts=which_parts)
-
-            if samples:
-                Ysim = self.posterior_samples_f(Xnew_indexed, samples, which_parts=which_parts, full_cov=True)
-                for yi in Ysim.T:
-                    ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25)
-
-            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)
-            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"
-            #if samples:
-            #    warnings.warn("Samples only implemented for 1 dimensional inputs.")
 
         else:
             raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
 
 
-    def plot_single_output(self, output=None, 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']):
+
+    def getstate(self):
         """
-        For a specific output, in a multioutput model, this function works just as plot_f on single output models.
+        Get the current state of the class, here we return everything that is needed to recompute the model.
-
-        :param output: which output to plot (for multiple output models only)
-        :type output: integer (first output is 0)
-        :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
-        :type plot_limits: np.array
-        :param which_data: which if the training data to plot (default all)
-        :type which_data: 'all' or a slice object to slice self.X, self.Y
-        :param which_parts: which of the kernel functions to plot (additively)
-        :type which_parts: 'all', or list of bools
-        :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
-        :type resolution: int
-        :param levels: number of levels to plot in a contour plot.
-        :type levels: int
-        :param samples: the number of a posteriori samples to plot
-        :type samples: int
-        :param fignum: figure to plot on.
-        :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
-        :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
         """
-        assert output is not None, "An output must be specified."
+        return Model.getstate(self) + [self.X,
-        assert len(self.likelihood.noise_model_list) > output, "The model has only %s outputs." %(self.output_dim + 1)
+                self.num_data,
-        if which_data == 'all':
+                self.input_dim,
-            which_data = slice(None)
+                self.kern,
+                self.likelihood,
+                self.output_dim,
+                self._Xoffset,
+                self._Xscale,
+                ]
 
-        if ax is None:
+    def setstate(self, state):
-            fig = pb.figure(num=fignum)
+        self._Xscale = state.pop()
-            ax = fig.add_subplot(111)
+        self._Xoffset = state.pop()
-
+        self.output_dim = state.pop()
-        if self.X.shape[1] == 2:
+        self.likelihood = state.pop()
-            resolution = resolution or 200
+        self.kern = state.pop()
-
+        self.input_dim = state.pop()
-            Xu = self.X[self.X[:,-1]==output,:] #keep the output of interest
+        self.num_data = state.pop()
-            Xu = self.X * self._Xscale + self._Xoffset
+        self.X = state.pop()
-            Xu = self.X[self.X[:,-1]==output ,0:1] #get rid of the index column
+        Model.setstate(self, state)
-
-            Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits)
-            Xnew_indexed = self._add_output_index(Xnew,output)
 
 
-            m, v, lower, upper = self.predict(Xnew_indexed, which_parts=which_parts,noise_model=output)
-
-            if samples: #NOTE not tested with fixed_inputs
-                Ysim = self.posterior_samples(Xnew_indexed, samples, which_parts=which_parts, full_cov=True,noise_model=output)
-                for yi in Ysim.T:
-                    ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25)
-
-            for d in range(m.shape[1]):
-                gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax, edgecol=linecol, fillcol=fillcol)
-                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 implemented for multioutput models with 2D inputs...yet"
-            #if samples:
-            #    warnings.warn("Samples only implemented for 1 dimensional inputs.")
-
-        else:
-            raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
-
-
-    def _add_output_index(self,X,output):
-        """
-        In a multioutput model, appends an index column to X to specify the output it is related to.
-
-        :param X: Input data
-        :type X: np.ndarray, N x self.input_dim
-        :param output: output X is related to
-        :type output: integer in {0,..., output_dim-1}
-
-        .. Note:: For multiple non-independent outputs models only.
-        """
-
-        assert hasattr(self,'multioutput'), 'This function is for multiple output models only.'
-
-        index = np.ones((X.shape[0],1))*output
-        return np.hstack((X,index))

GPy/core/sparse_gp.py

@@ -94,7 +94,6 @@ class SparseGP(GPBase):
 
         # factor Kmm
         self._Lm = jitchol(self.Kmm + self._const_jitter)
-        # TODO: no white kernel needed anymore, all noise in likelihood --------
 
         # The rather complex computations of self._A
         if self.has_uncertain_inputs:
@@ -204,27 +203,13 @@ class SparseGP(GPBase):
         D = 0.5 * self.data_fit
         return A + B + C + D + self.likelihood.Z
 
-    #def _set_params(self, p):
     def parameters_changed(self):
-        #self.Z = p[:self.num_inducing * self.input_dim].reshape(self.num_inducing, self.input_dim)
-        #self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.num_params])
-        #self.likelihood._set_params(p[self.Z.size + self.kern.num_params:])
         self._compute_kernel_matrices()
         self._computations()
         self.Cpsi1V = None
-        # make sparse_gp compatible with gp_base gradients:
         self.dL_dK = self.dL_dKmm
         super(SparseGP, self).parameters_changed()
 
-#     def _get_params(self):
-#         return np.hstack([self.Z.flatten(), self.kern._get_params_transformed(), self.likelihood._get_params()])
-# 
-#     def _get_param_names(self):
-#         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):
-    #    return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
 
     def update_likelihood_approximation(self, **kwargs):
         """
@@ -247,9 +232,6 @@ class SparseGP(GPBase):
                 # self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
                 self._set_params(self._get_params()) # update the GP
 
-#     def _log_likelihood_gradients(self):
-#         return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))
-
     def dL_dtheta(self):
         """
         Compute and return the derivative of the log marginal likelihood wrt the parameters of the kernel

GPy/models/gp_multioutput_regression.py

@@ -56,3 +56,117 @@ class GPMultioutputRegression(GP):
         self.multioutput = True
         GP.__init__(self, X, likelihood, mkernel, normalize_X=normalize_X)
         self.ensure_default_constraints()
+
+    def _add_output_index(self,X,output):
+        """
+        In a multioutput model, appends an index column to X to specify the output it is related to.
+
+        :param X: Input data
+        :type X: np.ndarray, N x self.input_dim
+        :param output: output X is related to
+        :type output: integer in {0,..., output_dim-1}
+
+        .. Note:: For multiple non-independent outputs models only.
+        """
+
+        assert hasattr(self,'multioutput'), 'This function is for multiple output models only.'
+
+        index = np.ones((X.shape[0],1))*output
+        return np.hstack((X,index))
+
+    def plot_single_output(self, X, output):
+        """
+        A simple wrapper around self.plot, with appropriate setting of the fixed_inputs argument
+        """
+        raise NotImplementedError
+
+    def _raw_predict_single_output(self, _Xnew, output, which_parts='all', full_cov=False,stop=False):
+        """
+        For a specific output, calls _raw_predict() at the new point(s) _Xnew.
+        This functions calls _add_output_index(), so _Xnew should not have an index column specifying the output.
+        ---------
+
+        :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,..., output_dim-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 non-independent outputs models only.
+        """
+        _Xnew = self._add_output_index(_Xnew, output)
+        return self._raw_predict(_Xnew, which_parts=which_parts,full_cov=full_cov, stop=stop)
+
+    def predict_single_output(self, Xnew,output=0, which_parts='all', full_cov=False, likelihood_args=dict()):
+        """
+        For a specific output, calls predict() at the new point(s) Xnew.
+        This functions calls _add_output_index(), so Xnew should not have an index column specifying the output.
+
+        :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 full covariance matrix, or just the diagonal
+        :type full_cov: bool
+        :returns: mean: posterior mean,  a Numpy array, Nnew x self.input_dim
+        :returns: var: 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 non-independent outputs models only.
+        """
+        Xnew = self._add_output_index(Xnew, output)
+        return self.predict(Xnew, which_parts=which_parts, full_cov=full_cov, likelihood_args=likelihood_args)
+
+    def plot_single_output_f(self, output=None, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, full_cov=False, fignum=None, ax=None):
+        """
+        For a specific output, in a multioutput model, this function works just as plot_f on single output models.
+
+        :param output: which output to plot (for multiple output models only)
+        :type output: integer (first output is 0)
+        :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
+        :param which_data: which if the training data to plot (default all)
+        :type which_data: 'all' or a slice object to slice self.X, self.Y
+        :param which_parts: which of the kernel functions to plot (additively)
+        :type which_parts: 'all', or list of bools
+        :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
+        :type resolution: int
+        :param full_cov:
+        :type full_cov: bool
+                :param fignum: figure to plot on.
+        :type fignum: figure number
+        :param ax: axes to plot on.
+        :type ax: axes handle
+        """
+        assert output is not None, "An output must be specified."
+        assert len(self.likelihood.noise_model_list) > output, "The model has only %s outputs." %(self.output_dim + 1)
+
+        if which_data == 'all':
+            which_data = slice(None)
+
+        if ax is None:
+            fig = pb.figure(num=fignum)
+            ax = fig.add_subplot(111)
+
+        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)
+            Xnew_indexed = self._add_output_index(Xnew,output)
+
+            m, v = self._raw_predict(Xnew_indexed, which_parts=which_parts)
+
+            if samples:
+                Ysim = self.posterior_samples_f(Xnew_indexed, samples, which_parts=which_parts, full_cov=True)
+                for yi in Ysim.T:
+                    ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25)
+
+            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)
+            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)
+
+