mirror of
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Merge branch 'devel' into params
This commit is contained in:
Max Zwiessele
commit
4f56506aa6
60 changed files with 1944 additions and 596 deletions
8
GPy/FAQ.txt
Normal file
8
GPy/FAQ.txt
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|
|
@ -0,0 +1,8 @@
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Frequently Asked Questions
|
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--------------------------
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|
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Unit tests are run through Travis-Ci. They can be run locally through entering the GPy route diretory and writing
|
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|
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nosetests testing/
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||||
|
||||
Documentation is handled by Sphinx. To build the documentation:
|
||||
10
GPy/coding_style_guide.txt
Normal file
10
GPy/coding_style_guide.txt
Normal file
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@ -0,0 +1,10 @@
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In this text document we will describe coding conventions to be used in GPy to keep things consistent.
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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.
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Input matrices are either X or t, output matrices are Y.
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Input dimensionality is input_dim, output dimensionality is output_dim, number of data is num_data.
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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.
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@ -11,25 +11,27 @@ from sparse_gp import SparseGP
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class FITC(SparseGP):
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"""
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sparse FITC approximation
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Sparse FITC approximation
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:param X: inputs
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:type X: np.ndarray (num_data x Q)
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:param likelihood: a likelihood instance, containing the observed data
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:type likelihood: GPy.likelihood.(Gaussian | EP)
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:param kernel : the kernel (covariance function). See link kernels
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:param kernel: the kernel (covariance function). See link kernels
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:type kernel: a GPy.kern.kern instance
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:param Z: inducing inputs (optional, see note)
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:type Z: np.ndarray (M x Q) | None
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:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
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:param normalize_(X|Y): whether to normalize the data before computing (predictions will be in original scales)
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:type normalize_(X|Y): bool
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|
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"""
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def __init__(self, X, likelihood, kernel, Z, normalize_X=False):
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SparseGP.__init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False)
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assert self.output_dim == 1, "FITC model is not defined for handling multiple outputs"
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|
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def update_likelihood_approximation(self):
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def update_likelihood_approximation(self, **kwargs):
|
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"""
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Approximates a non-Gaussian likelihood using Expectation Propagation
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@ -37,7 +39,7 @@ class FITC(SparseGP):
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this function does nothing
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"""
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self.likelihood.restart()
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self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
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self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0, **kwargs)
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self._set_params(self._get_params())
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def _compute_kernel_matrices(self):
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|
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@ -120,7 +122,7 @@ class FITC(SparseGP):
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_dKmm = .5*(V_n**2 + alpha_n + gamma_n**2 - 2.*gamma_k) * K_pp_K #Diag_dD_dKmm
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self._dpsi1_dtheta += self.kern.dK_dtheta(_dpsi1,self.X[i:i+1,:],self.Z)
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self._dKmm_dtheta += self.kern.dK_dtheta(_dKmm,self.Z)
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self._dKmm_dX += 2.*self.kern.dK_dX(_dKmm ,self.Z)
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self._dKmm_dX += self.kern.dK_dX(_dKmm ,self.Z)
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self._dpsi1_dX += self.kern.dK_dX(_dpsi1.T,self.Z,self.X[i:i+1,:])
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# the partial derivative vector for the likelihood
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|
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|
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@ -15,7 +15,7 @@ class GP(GPBase):
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|
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:param X: input observations
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:param kernel: a GPy kernel, defaults to rbf+white
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:parm likelihood: a GPy likelihood
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:param likelihood: a GPy likelihood
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:param normalize_X: whether to normalize the input data before computing (predictions will be in original scales)
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:type normalize_X: False|True
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:rtype: model object
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@ -62,7 +62,7 @@ class GP(GPBase):
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def _get_param_names(self):
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return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
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|
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def update_likelihood_approximation(self):
|
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def update_likelihood_approximation(self, **kwargs):
|
||||
"""
|
||||
Approximates a non-gaussian likelihood using Expectation Propagation
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||||
|
||||
|
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@ -70,7 +70,7 @@ class GP(GPBase):
|
|||
this function does nothing
|
||||
"""
|
||||
self.likelihood.restart()
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self.likelihood.fit_full(self.kern.K(self.X))
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self.likelihood.fit_full(self.kern.K(self.X), **kwargs)
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self._set_params(self._get_params()) # update the GP
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def _model_fit_term(self):
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|
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@ -132,17 +132,16 @@ class GP(GPBase):
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|||
def predict(self, Xnew, which_parts='all', full_cov=False, likelihood_args=dict()):
|
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"""
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Predict the function(s) at the new point(s) Xnew.
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Arguments
|
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---------
|
||||
|
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:param Xnew: The points at which to make a prediction
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:type Xnew: np.ndarray, Nnew x self.input_dim
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:param which_parts: specifies which outputs kernel(s) to use in prediction
|
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:type which_parts: ('all', list of bools)
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||||
:param full_cov: whether to return the full covariance matrix, or just the diagonal
|
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:type full_cov: bool
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:rtype: posterior mean, a Numpy array, Nnew x self.input_dim
|
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: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
|
||||
:returns: mean: posterior mean, a Numpy array, Nnew x self.input_dim
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:returns: var: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
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:returns: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim
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|
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|
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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.
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|
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@ -160,8 +159,7 @@ class GP(GPBase):
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def predict_single_output(self, Xnew, output=0, which_parts='all', full_cov=False):
|
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"""
|
||||
For a specific output, predict the function at the new point(s) Xnew.
|
||||
Arguments
|
||||
---------
|
||||
|
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:param Xnew: The points at which to make a prediction
|
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:type Xnew: np.ndarray, Nnew x self.input_dim
|
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:param output: output to predict
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|
|
@ -170,9 +168,9 @@ class GP(GPBase):
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|||
:type which_parts: ('all', list of bools)
|
||||
:param full_cov: whether to return the full covariance matrix, or just the diagonal
|
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:type full_cov: bool
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:rtype: posterior mean, a Numpy array, Nnew x self.input_dim
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: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
|
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: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
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:returns: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim
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|
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.. Note:: For multiple output models only
|
||||
"""
|
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|
|
|
|||
|
|
@ -128,10 +128,9 @@ class GPBase(Model):
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else:
|
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raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
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||||
else:
|
||||
assert self.num_outputs > output, 'The model has only %s outputs.' %self.num_outputs
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assert len(self.likelihood.noise_model_list) > output, 'The model has only %s outputs.' %self.num_outputs
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|
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if self.X.shape[1] == 2:
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assert self.num_outputs >= output, 'The model has only %s outputs.' %self.num_outputs
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Xu = self.X[self.X[:,-1]==output ,0:1]
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||||
Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits)
|
||||
|
||||
|
|
@ -263,7 +262,7 @@ class GPBase(Model):
|
|||
raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
|
||||
|
||||
else:
|
||||
assert self.num_outputs > output, 'The model has only %s outputs.' %self.num_outputs
|
||||
assert len(self.likelihood.noise_model_list) > output, 'The model has only %s outputs.' %self.num_outputs
|
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if self.X.shape[1] == 2:
|
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resolution = resolution or 200
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Xu = self.X[self.X[:,-1]==output,:] #keep the output of interest
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|
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@ -287,3 +286,20 @@ class GPBase(Model):
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|||
|
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else:
|
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raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
|
||||
|
||||
"""
|
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def samples_f(self,X,samples=10, which_data='all', which_parts='all',output=None):
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if which_data == 'all':
|
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which_data = slice(None)
|
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|
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if hasattr(self,'multioutput'):
|
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np.hstack([X,np.ones((X.shape[0],1))*output])
|
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|
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m, v = self._raw_predict(X, which_parts=which_parts, full_cov=True)
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v = v.reshape(m.size,-1) if len(v.shape)==3 else v
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Ysim = np.random.multivariate_normal(m.flatten(), v, samples)
|
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#gpplot(X, m, m - 2 * np.sqrt(np.diag(v)[:, None]), m + 2 * np.sqrt(np.diag(v))[:, None, ], axes=ax)
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for i in range(samples):
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ax.plot(X, Ysim[i, :], Tango.colorsHex['darkBlue'], linewidth=0.25)
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||||
|
||||
"""
|
||||
|
|
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@ -49,6 +49,7 @@ class Mapping(Parameterized):
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|||
|
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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']):
|
||||
"""
|
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Plot the mapping.
|
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|
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Plots the mapping associated with the model.
|
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|
|
@ -79,8 +80,7 @@ class Mapping(Parameterized):
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:type fixed_inputs: a list of tuples
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:param linecol: color of line to plot.
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:type linecol:
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:param levels: for 2D plotting, the number of contour levels to use
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is ax is None, create a new figure
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:param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
|
||||
|
||||
"""
|
||||
# TODO include samples
|
||||
|
|
|
|||
|
|
@ -47,6 +47,7 @@ class Model(Parameterized):
|
|||
|
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:param state: the state of the model.
|
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:type state: list as returned from getstate.
|
||||
|
||||
"""
|
||||
self.preferred_optimizer = state.pop()
|
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self.sampling_runs = state.pop()
|
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|
|
@ -56,10 +57,11 @@ class Model(Parameterized):
|
|||
|
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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)
|
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: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
|
||||
set to the number of processors on the current machine.
|
||||
|
||||
.. 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.
|
||||
|
||||
"""
|
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initial_parameters = self._get_params_transformed()
|
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|
|
@ -538,22 +540,17 @@ class Model(Parameterized):
|
|||
return k.variances
|
||||
|
||||
|
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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:
|
||||
|
||||
: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?
|
||||
:param stop_crit: convergence criterion
|
||||
:type stop_crit: float
|
||||
|
||||
.. Note: kwargs are passed to update_likelihood and optimize functions.
|
||||
"""
|
||||
assert isinstance(self.likelihood, likelihoods.EP) or isinstance(self.likelihood, likelihoods.EP_Mixed_Noise), "pseudo_EM is only available for EP likelihoods"
|
||||
ll_change = epsilon + 1.
|
||||
ll_change = stop_crit + 1.
|
||||
iteration = 0
|
||||
last_ll = -np.inf
|
||||
|
||||
|
|
@ -561,10 +558,25 @@ 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()
|
||||
self.update_likelihood_approximation()
|
||||
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
|
||||
|
||||
|
|
@ -576,7 +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:
|
||||
|
|
|
|||
|
|
@ -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()))
|
||||
|
|
|
|||
|
|
@ -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):
|
||||
|
|
@ -215,7 +216,7 @@ class SparseGP(GPBase):
|
|||
#def _get_print_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
|
||||
|
||||
|
|
@ -229,10 +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
|
||||
|
||||
|
|
@ -292,7 +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:
|
||||
|
|
@ -306,10 +307,11 @@ 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
|
||||
|
|
@ -365,9 +367,8 @@ class SparseGP(GPBase):
|
|||
ax.plot(Zu[:, 0], Zu[:, 1], 'wo')
|
||||
|
||||
else:
|
||||
pass
|
||||
"""
|
||||
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
|
||||
|
|
@ -378,6 +379,7 @@ class SparseGP(GPBase):
|
|||
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] #??
|
||||
|
|
@ -386,13 +388,11 @@ class SparseGP(GPBase):
|
|||
|
||||
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.
|
||||
Arguments
|
||||
---------
|
||||
|
||||
:param Xnew: The points at which to make a prediction
|
||||
:type Xnew: np.ndarray, Nnew x self.input_dim
|
||||
:param output: output to predict
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
||||
"""
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -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)
|
||||
|
|
@ -118,61 +102,13 @@ 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):
|
||||
"""
|
||||
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.
|
||||
|
||||
: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.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):
|
||||
"""
|
||||
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
|
||||
|
||||
|
||||
def toy_heaviside(seed=default_seed):
|
||||
"""
|
||||
Simple 1D classification example using a heavy side gp transformation
|
||||
: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)
|
||||
|
|
@ -198,3 +134,35 @@ def toy_heaviside(seed=default_seed):
|
|||
|
||||
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 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
|
||||
|
||||
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.
|
||||
|
||||
elif model_type == 'FITC':
|
||||
m = GPy.models.FITCClassification(data['X'], Y, kernel=kernel, num_inducing=num_inducing)
|
||||
m['.*len'] = 3.
|
||||
|
||||
m.pseudo_EM()
|
||||
print(m)
|
||||
m.plot()
|
||||
|
||||
return m
|
||||
|
|
|
|||
|
|
@ -132,7 +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, :]
|
||||
|
||||
|
|
|
|||
|
|
@ -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)
|
||||
df(xi, *args, **kwargs)
|
||||
f(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)
|
||||
df(xi, *args, **kwargs)
|
||||
f(xi, \*args, \*\*kwargs)
|
||||
df(xi, \*args, \*\*kwargs)
|
||||
|
||||
**returns**
|
||||
---------
|
||||
|
||||
x_opt, f_opt, g_opt, iteration, function_calls, gradient_calls, status_message
|
||||
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
@ -128,6 +129,8 @@ 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_iters, **opt_dict)
|
||||
|
|
|
|||
|
|
@ -10,11 +10,10 @@ class opt_SGD(Optimizer):
|
|||
"""
|
||||
Optimize using stochastic gradient descent.
|
||||
|
||||
*** Parameters ***
|
||||
Model: reference to the Model object
|
||||
iterations: number of iterations
|
||||
learning_rate: learning rate
|
||||
momentum: momentum
|
||||
:param Model: reference to the Model object
|
||||
:param iterations: number of iterations
|
||||
:param learning_rate: learning rate
|
||||
:param momentum: momentum
|
||||
|
||||
"""
|
||||
|
||||
|
|
|
|||
|
|
@ -17,6 +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])
|
||||
|
|
@ -33,6 +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])
|
||||
|
|
@ -41,11 +43,13 @@ def linear(input_dim,variances=None,ARD=False):
|
|||
"""
|
||||
Construct a linear kernel.
|
||||
|
||||
Arguments
|
||||
---------
|
||||
input_dimD (int), obligatory
|
||||
variances (np.ndarray)
|
||||
ARD (boolean)
|
||||
:param input_dim: dimensionality of the kernel, obligatory
|
||||
:type input_dim: int
|
||||
:param variances:
|
||||
:type variances: np.ndarray
|
||||
: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])
|
||||
|
|
@ -64,39 +68,42 @@ 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.
|
||||
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.
|
||||
Where :math:`l(x)` is a function giving the length scale as a function of space.
|
||||
|
||||
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.
|
||||
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.
|
||||
|
||||
:param input_dim: the number of input dimensions
|
||||
:type input_dim: int
|
||||
: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.
|
||||
:type ARD: Boolean
|
||||
:rtype: Kernpart object
|
||||
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`
|
||||
: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 :math:`\\sigma^2_w`), otherwise there is one weight variance parameter per dimension.
|
||||
:type ARD: Boolean
|
||||
:rtype: Kernpart object
|
||||
|
||||
"""
|
||||
part = parts.gibbs.Gibbs(input_dim,variance,mapping)
|
||||
|
|
@ -124,6 +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])
|
||||
|
|
@ -132,14 +140,42 @@ def white(input_dim,variance=1.):
|
|||
"""
|
||||
Construct a white kernel.
|
||||
|
||||
Arguments
|
||||
---------
|
||||
input_dimD (int), obligatory
|
||||
variance (float)
|
||||
:param input_dim: dimensionality of the kernel, obligatory
|
||||
:type input_dim: int
|
||||
:param variance: the variance of the kernel
|
||||
: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):
|
||||
"""
|
||||
|
|
@ -153,6 +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])
|
||||
|
|
@ -169,6 +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])
|
||||
|
|
@ -185,6 +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])
|
||||
|
|
@ -193,10 +232,11 @@ def bias(input_dim, variance=1.):
|
|||
"""
|
||||
Construct a bias kernel.
|
||||
|
||||
Arguments
|
||||
---------
|
||||
input_dim (int), obligatory
|
||||
variance (float)
|
||||
:param input_dim: dimensionality of the kernel, obligatory
|
||||
:type input_dim: int
|
||||
:param variance: the variance of the kernel
|
||||
:type variance: float
|
||||
|
||||
"""
|
||||
part = parts.bias.Bias(input_dim, variance)
|
||||
return kern(input_dim, [part])
|
||||
|
|
@ -204,10 +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
|
||||
G: np.array with shape (n,n) - the Gram matrix associated to F
|
||||
variances : np.ndarray with shape (n,)
|
||||
|
||||
:param input_dim: the number of input dimensions
|
||||
:type input_dim: int
|
||||
: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])
|
||||
|
|
@ -220,6 +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])
|
||||
|
|
@ -232,43 +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)]
|
||||
dist_string = ' + '.join(['(x%i-z%i)**2/rbf_lengthscale_%i**2' % (i, i, i) 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/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))
|
||||
return kern(input_dim, [spkern(input_dim, f)])
|
||||
f = variance*sp.exp(-dist/(2*lengthscale**2))
|
||||
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):
|
||||
|
|
@ -285,6 +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])
|
||||
|
|
@ -303,6 +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])
|
||||
|
|
@ -321,6 +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])
|
||||
|
|
@ -334,6 +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])
|
||||
|
|
@ -346,30 +431,32 @@ def symmetric(k):
|
|||
k_.parts = [symmetric.Symmetric(p) for p in k.parts]
|
||||
return k_
|
||||
|
||||
def coregionalize(num_outputs,W_columns=1, W=None, kappa=None):
|
||||
def coregionalize(output_dim,rank=1, W=None, kappa=None):
|
||||
"""
|
||||
Coregionlization matrix B, of the form:
|
||||
|
||||
.. math::
|
||||
\mathbf{B} = \mathbf{W}\mathbf{W}^\top + kappa \mathbf{I}
|
||||
|
||||
An intrinsic/linear coregionalization kernel of the form
|
||||
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 num_outputs: the number of outputs to coregionalize
|
||||
:type num_outputs: int
|
||||
:param W_columns: number of columns of the W matrix (this parameter is ignored if parameter W is not None)
|
||||
:type W_colunns: int
|
||||
:param output_dim: the number of outputs to corregionalize
|
||||
:type output_dim: int
|
||||
: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 coregionalization matrix B
|
||||
:type W: numpy array of dimensionality (num_outpus, W_columns)
|
||||
:type W: numpy array of dimensionality (num_outpus, rank)
|
||||
:param kappa: a vector which allows the outputs to behave independently
|
||||
:type kappa: numpy array of dimensionality (num_outputs,)
|
||||
:type kappa: numpy array of dimensionality (output_dim,)
|
||||
:rtype: kernel object
|
||||
|
||||
"""
|
||||
p = parts.coregionalize.Coregionalize(num_outputs,W_columns,W,kappa)
|
||||
p = parts.coregionalize.Coregionalize(output_dim,rank,W,kappa)
|
||||
return kern(1,[p])
|
||||
|
||||
|
||||
|
|
@ -422,25 +509,26 @@ 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, num_outputs, kernel_list = [], W_columns=1,W=None,kappa=None):
|
||||
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
|
||||
:num_outputs: Number of outputs
|
||||
: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 W_columns: number tuples of the corregionalization parameters 'coregion_W'
|
||||
:type W_columns: integer
|
||||
:param rank: number tuples of the corregionalization parameters 'coregion_W'
|
||||
:type rank: integer
|
||||
|
||||
..note the kernels dimensionality is overwritten to fit input_dim
|
||||
|
||||
..Note the kernels dimensionality is overwritten to fit input_dim
|
||||
"""
|
||||
|
||||
for k in kernel_list:
|
||||
|
|
@ -448,11 +536,31 @@ def build_lcm(input_dim, num_outputs, kernel_list = [], W_columns=1,W=None,kappa
|
|||
k.input_dim = input_dim
|
||||
warnings.warn("kernel's input dimension overwritten to fit input_dim parameter.")
|
||||
|
||||
k_coreg = coregionalize(num_outputs,W_columns,W,kappa)
|
||||
k_coreg = coregionalize(output_dim,rank,W,kappa)
|
||||
kernel = kernel_list[0]**k_coreg.copy()
|
||||
|
||||
for k in kernel_list[1:]:
|
||||
k_coreg = coregionalize(num_outputs,W_columns,W,kappa)
|
||||
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])
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
@ -79,13 +80,15 @@ 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)
|
||||
|
|
@ -176,8 +179,10 @@ 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
|
||||
|
|
@ -219,11 +224,13 @@ 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()
|
||||
|
|
@ -322,6 +329,7 @@ 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)
|
||||
|
|
@ -341,6 +349,7 @@ 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)"""
|
||||
|
||||
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)]
|
||||
|
|
@ -414,6 +423,7 @@ 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)]
|
||||
|
|
@ -568,7 +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
|
||||
|
|
@ -657,6 +667,7 @@ 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:
|
||||
|
|
@ -683,7 +694,7 @@ def kern_test(kern, X=None, X2=None, verbose=False):
|
|||
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)
|
||||
|
|
@ -694,7 +705,7 @@ def kern_test(kern, X=None, X2=None, verbose=False):
|
|||
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)
|
||||
|
|
@ -705,10 +716,15 @@ def kern_test(kern, X=None, X2=None, verbose=False):
|
|||
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.")
|
||||
result = Kern_check_dK_dX(kern, X=X, X2=None).checkgrad(verbose=verbose)
|
||||
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:
|
||||
|
|
@ -719,7 +735,12 @@ def kern_test(kern, X=None, X2=None, verbose=False):
|
|||
|
||||
if verbose:
|
||||
print("Checking gradients of K(X, X2) wrt X.")
|
||||
result = Kern_check_dK_dX(kern, X=X, X2=X2).checkgrad(verbose=verbose)
|
||||
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:
|
||||
|
|
@ -730,7 +751,12 @@ def kern_test(kern, X=None, X2=None, verbose=False):
|
|||
|
||||
if verbose:
|
||||
print("Checking gradients of Kdiag(X) wrt X.")
|
||||
result = Kern_check_dKdiag_dX(kern, X=X).checkgrad(verbose=verbose)
|
||||
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:
|
||||
|
|
@ -738,5 +764,5 @@ def kern_test(kern, X=None, X2=None, verbose=False):
|
|||
Kern_check_dKdiag_dX(kern, X=X).checkgrad(verbose=True)
|
||||
pass_checks = False
|
||||
return False
|
||||
|
||||
|
||||
return pass_checks
|
||||
|
|
|
|||
161
GPy/kern/parts/ODE_1.py
Normal file
161
GPy/kern/parts/ODE_1.py
Normal file
|
|
@ -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
|
||||
|
|
@ -2,16 +2,18 @@ import bias
|
|||
import Brownian
|
||||
import coregionalize
|
||||
import exponential
|
||||
import eq_ode1
|
||||
import finite_dimensional
|
||||
import fixed
|
||||
import gibbs
|
||||
#import hetero #hetero.py is not commited: omitting for now. JH.
|
||||
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
|
||||
|
|
|
|||
|
|
@ -11,44 +11,47 @@ class Coregionalize(Kernpart):
|
|||
"""
|
||||
Covariance function for intrinsic/linear coregionalization models
|
||||
|
||||
This covariance has the form
|
||||
This covariance has the form:
|
||||
.. math::
|
||||
\mathbf{B} = \mathbf{W}\mathbf{W}^\top + kappa \mathbf{I}
|
||||
\mathbf{B} = \mathbf{W}\mathbf{W}^\top + \text{diag}(kappa)
|
||||
|
||||
An intrinsic/linear coregionalization covariance function of the form
|
||||
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 num_outputs: number of outputs to coregionalize
|
||||
:type num_outputs: int
|
||||
:param W_columns: number of columns of the W matrix (this parameter is ignored if parameter W is not None)
|
||||
:type W_colunns: int
|
||||
:param output_dim: number of outputs to coregionalize
|
||||
:type output_dim: int
|
||||
: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 coregionalization matrix B
|
||||
:type W: numpy array of dimensionality (num_outpus, W_columns)
|
||||
:param kappa: a vector which allows the outputs to behave independently
|
||||
:type kappa: numpy array of dimensionality (num_outputs,)
|
||||
:type kappa: numpy array of dimensionality (output_dim,)
|
||||
|
||||
.. Note: see coregionalization examples in GPy.examples.regression for some usage.
|
||||
.. note: see coregionalization examples in GPy.examples.regression for some usage.
|
||||
"""
|
||||
def __init__(self,num_outputs,W_columns=1, W=None, kappa=None):
|
||||
def __init__(self, output_dim, rank=1, W=None, kappa=None):
|
||||
self.input_dim = 1
|
||||
self.name = 'coregion'
|
||||
self.num_outputs = num_outputs
|
||||
self.W_columns = W_columns
|
||||
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.num_outputs,self.W_columns)/np.sqrt(self.W_columns)
|
||||
self.W = 0.5*np.random.randn(self.output_dim,self.rank)/np.sqrt(self.rank)
|
||||
else:
|
||||
assert W.shape==(self.num_outputs,self.W_columns)
|
||||
assert W.shape==(self.output_dim,self.rank)
|
||||
self.W = W
|
||||
if kappa is None:
|
||||
kappa = 0.5*np.ones(self.num_outputs)
|
||||
kappa = 0.5*np.ones(self.output_dim)
|
||||
else:
|
||||
assert kappa.shape==(self.num_outputs,)
|
||||
assert kappa.shape==(self.output_dim,)
|
||||
self.kappa = kappa
|
||||
self.num_params = self.num_outputs*(self.W_columns + 1)
|
||||
self.num_params = self.output_dim*(self.rank + 1)
|
||||
self._set_params(np.hstack([self.W.flatten(),self.kappa]))
|
||||
|
||||
def _get_params(self):
|
||||
|
|
@ -56,12 +59,12 @@ class Coregionalize(Kernpart):
|
|||
|
||||
def _set_params(self,x):
|
||||
assert x.size == self.num_params
|
||||
self.kappa = x[-self.num_outputs:]
|
||||
self.W = x[:-self.num_outputs].reshape(self.num_outputs,self.W_columns)
|
||||
self.kappa = x[-self.output_dim:]
|
||||
self.W = x[:-self.output_dim].reshape(self.output_dim,self.rank)
|
||||
self.B = np.dot(self.W,self.W.T) + np.diag(self.kappa)
|
||||
|
||||
def _get_param_names(self):
|
||||
return sum([['W%i_%i'%(i,j) for j in range(self.W_columns)] for i in range(self.num_outputs)],[]) + ['kappa_%i'%i for i in range(self.num_outputs)]
|
||||
return sum([['W%i_%i'%(i,j) for j in range(self.rank)] for i in range(self.output_dim)],[]) + ['kappa_%i'%i for i in range(self.output_dim)]
|
||||
|
||||
def K(self,index,index2,target):
|
||||
index = np.asarray(index,dtype=np.int)
|
||||
|
|
@ -79,26 +82,26 @@ class Coregionalize(Kernpart):
|
|||
if index2 is None:
|
||||
code="""
|
||||
for(int i=0;i<N; i++){
|
||||
target[i+i*N] += B[index[i]+num_outputs*index[i]];
|
||||
target[i+i*N] += B[index[i]+output_dim*index[i]];
|
||||
for(int j=0; j<i; j++){
|
||||
target[j+i*N] += B[index[i]+num_outputs*index[j]];
|
||||
target[j+i*N] += B[index[i]+output_dim*index[j]];
|
||||
target[i+j*N] += target[j+i*N];
|
||||
}
|
||||
}
|
||||
"""
|
||||
N,B,num_outputs = index.size, self.B, self.num_outputs
|
||||
weave.inline(code,['target','index','N','B','num_outputs'])
|
||||
N,B,output_dim = index.size, self.B, self.output_dim
|
||||
weave.inline(code,['target','index','N','B','output_dim'])
|
||||
else:
|
||||
index2 = np.asarray(index2,dtype=np.int)
|
||||
code="""
|
||||
for(int i=0;i<num_inducing; i++){
|
||||
for(int j=0; j<N; j++){
|
||||
target[i+j*num_inducing] += B[num_outputs*index[j]+index2[i]];
|
||||
target[i+j*num_inducing] += B[output_dim*index[j]+index2[i]];
|
||||
}
|
||||
}
|
||||
"""
|
||||
N,num_inducing,B,num_outputs = index.size,index2.size, self.B, self.num_outputs
|
||||
weave.inline(code,['target','index','index2','N','num_inducing','B','num_outputs'])
|
||||
N,num_inducing,B,output_dim = index.size,index2.size, self.B, self.output_dim
|
||||
weave.inline(code,['target','index','index2','N','num_inducing','B','output_dim'])
|
||||
|
||||
|
||||
def Kdiag(self,index,target):
|
||||
|
|
@ -115,12 +118,12 @@ class Coregionalize(Kernpart):
|
|||
code="""
|
||||
for(int i=0; i<num_inducing; i++){
|
||||
for(int j=0; j<N; j++){
|
||||
dL_dK_small[index[j] + num_outputs*index2[i]] += dL_dK[i+j*num_inducing];
|
||||
dL_dK_small[index[j] + output_dim*index2[i]] += dL_dK[i+j*num_inducing];
|
||||
}
|
||||
}
|
||||
"""
|
||||
N, num_inducing, num_outputs = index.size, index2.size, self.num_outputs
|
||||
weave.inline(code, ['N','num_inducing','num_outputs','dL_dK','dL_dK_small','index','index2'])
|
||||
N, num_inducing, output_dim = index.size, index2.size, self.output_dim
|
||||
weave.inline(code, ['N','num_inducing','output_dim','dL_dK','dL_dK_small','index','index2'])
|
||||
|
||||
dkappa = np.diag(dL_dK_small)
|
||||
dL_dK_small += dL_dK_small.T
|
||||
|
|
@ -137,8 +140,8 @@ class Coregionalize(Kernpart):
|
|||
ii,jj = ii.T, jj.T
|
||||
|
||||
dL_dK_small = np.zeros_like(self.B)
|
||||
for i in range(self.num_outputs):
|
||||
for j in range(self.num_outputs):
|
||||
for i in range(self.output_dim):
|
||||
for j in range(self.output_dim):
|
||||
tmp = np.sum(dL_dK[(ii==i)*(jj==j)])
|
||||
dL_dK_small[i,j] = tmp
|
||||
|
||||
|
|
@ -150,8 +153,8 @@ class Coregionalize(Kernpart):
|
|||
|
||||
def dKdiag_dtheta(self,dL_dKdiag,index,target):
|
||||
index = np.asarray(index,dtype=np.int).flatten()
|
||||
dL_dKdiag_small = np.zeros(self.num_outputs)
|
||||
for i in range(self.num_outputs):
|
||||
dL_dKdiag_small = np.zeros(self.output_dim)
|
||||
for i in range(self.output_dim):
|
||||
dL_dKdiag_small[i] += np.sum(dL_dKdiag[index==i])
|
||||
dW = 2.*self.W*dL_dKdiag_small[:,None]
|
||||
dkappa = dL_dKdiag_small
|
||||
|
|
|
|||
556
GPy/kern/parts/eq_ode1.py
Normal file
556
GPy/kern/parts/eq_ode1.py
Normal file
|
|
@ -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
|
||||
|
|
@ -10,9 +10,12 @@ 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.
|
||||
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.
|
||||
Heteroschedastic noise which depends on input location. See, for example,
|
||||
this paper by Goldberg et al.
|
||||
|
||||
.. math::
|
||||
|
||||
|
|
@ -20,15 +23,15 @@ class Hetero(Kernpart):
|
|||
|
||||
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.
|
||||
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
|
||||
: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:
|
||||
|
||||
|
|
@ -36,7 +39,7 @@ class Hetero(Kernpart):
|
|||
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.
|
||||
|
||||
"""
|
||||
|
|
@ -47,7 +50,7 @@ class Hetero(Kernpart):
|
|||
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'
|
||||
|
|
@ -66,7 +69,7 @@ class Hetero(Kernpart):
|
|||
|
||||
def K(self, X, X2, target):
|
||||
"""Return covariance between X and X2."""
|
||||
if X2==None or X2 is X:
|
||||
if (X2 is None) or (X2 is X):
|
||||
target[np.diag_indices_from(target)] += self._Kdiag(X)
|
||||
|
||||
def Kdiag(self, X, target):
|
||||
|
|
@ -76,26 +79,26 @@ class Hetero(Kernpart):
|
|||
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==None or X2 is X:
|
||||
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], X)*self.mapping.f(X)
|
||||
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)
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -58,6 +58,8 @@ 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
|
||||
|
||||
|
||||
|
||||
|
|
@ -97,6 +99,9 @@ class Kernpart_stationary(Kernpart):
|
|||
# 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):
|
||||
|
|
|
|||
|
|
@ -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):
|
||||
|
|
|
|||
38
GPy/kern/parts/odekern1.c
Normal file
38
GPy/kern/parts/odekern1.c
Normal file
|
|
@ -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;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
@ -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,
|
||||
.. math::
|
||||
|
||||
k(x, y) = \sigma^2*(\sigma_w^2 x'y+\sigma_b^b)^d
|
||||
|
||||
The kernel parameters are \sigma^2 (variance), \sigma^2_w
|
||||
(weight_variance), \sigma^2_b (bias_variance) and d
|
||||
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
|
||||
|
||||
The kernel parameters are :math:`\sigma^2` (variance), :math:`\sigma^2_w`
|
||||
(weight_variance), :math:`\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
|
||||
|
||||
|
|
|
|||
|
|
@ -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);
|
||||
}
|
||||
|
|
|
|||
|
|
@ -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);
|
||||
|
|
|
|||
|
|
@ -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):
|
||||
self.name='sympykern'
|
||||
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
|
||||
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]\
|
||||
+ ["param[%i]"%i for i in range(self.num_params)])
|
||||
# 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]
|
||||
+ ["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;
|
||||
|
|
@ -192,30 +209,34 @@ class spkern(Kernpart):
|
|||
int input_dim = X_array->dimensions[1];
|
||||
//#pragma omp parallel for private(j)
|
||||
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);}
|
||||
|
||||
}
|
||||
for (j=0; j<num_inducing; j++){
|
||||
%s
|
||||
}
|
||||
}
|
||||
%s
|
||||
"""%(gradient_funcs,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
|
||||
|
||||
# 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[')
|
||||
|
||||
#now for gradients of Kdiag wrt X
|
||||
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++){
|
||||
j = i;
|
||||
for (int i=0;i<N; 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
|
||||
|
|
@ -223,7 +244,10 @@ class spkern(Kernpart):
|
|||
|
||||
def K(self,X,Z,target):
|
||||
param = self._param
|
||||
weave.inline(self._K_code,arg_names=['target','X','Z','param'],**self.weave_kwargs)
|
||||
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):
|
||||
param = self._param
|
||||
|
|
@ -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','Z','param','partial'],**self.weave_kwargs)
|
||||
weave.inline(self._dKdiag_dtheta_code,arg_names=['target','X','param','partial'],**self.weave_kwargs)
|
||||
|
||||
def dK_dX(self,partial,X,Z,target):
|
||||
param = self._param
|
||||
weave.inline(self._dK_dX_code,arg_names=['target','X','Z','param','partial'],**self.weave_kwargs)
|
||||
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','Z','param','partial'],**self.weave_kwargs)
|
||||
weave.inline(self._dKdiag_dX_code,arg_names=['target','X','param','partial'],**self.weave_kwargs)
|
||||
|
||||
def _set_params(self,param):
|
||||
#print param.flags['C_CONTIGUOUS']
|
||||
|
|
|
|||
|
|
@ -4,33 +4,32 @@ from ..util.linalg import pdinv,mdot,jitchol,chol_inv,DSYR,tdot,dtrtrs
|
|||
from likelihood import likelihood
|
||||
|
||||
class EP(likelihood):
|
||||
def __init__(self,data,noise_model,epsilon=1e-3,power_ep=[1.,1.]):
|
||||
def __init__(self,data,noise_model):
|
||||
"""
|
||||
Expectation Propagation
|
||||
|
||||
Arguments
|
||||
---------
|
||||
epsilon : Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float)
|
||||
noise_model : a likelihood function (see likelihood_functions.py)
|
||||
:param data: data to model
|
||||
:type data: numpy array
|
||||
:param noise_model: noise distribution
|
||||
:type noise_model: A GPy noise model
|
||||
|
||||
"""
|
||||
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.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.v_tilde = np.zeros(self.N)
|
||||
self.tau_tilde = np.zeros(self.num_data)
|
||||
self.v_tilde = np.zeros(self.num_data)
|
||||
|
||||
#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.Y = np.zeros((self.num_data,1))
|
||||
self.covariance_matrix = np.eye(self.num_data)
|
||||
self.precision = np.ones(self.num_data)[:,None]
|
||||
self.Z = 0
|
||||
self.YYT = None
|
||||
self.V = self.precision * self.Y
|
||||
|
|
@ -40,11 +39,11 @@ class EP(likelihood):
|
|||
super(EP, self).__init__()
|
||||
|
||||
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.tau_tilde = np.zeros(self.num_data)
|
||||
self.v_tilde = np.zeros(self.num_data)
|
||||
self.Y = np.zeros((self.num_data,1))
|
||||
self.covariance_matrix = np.eye(self.num_data)
|
||||
self.precision = np.ones(self.num_data)[:,None]
|
||||
self.Z = 0
|
||||
self.YYT = None
|
||||
self.V = self.precision * self.Y
|
||||
|
|
@ -78,6 +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)
|
||||
|
|
@ -87,13 +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()
|
||||
|
||||
"""
|
||||
|
|
@ -102,15 +111,15 @@ class EP(likelihood):
|
|||
sigma_ = 1./tau_
|
||||
mu_ = v_/tau_
|
||||
"""
|
||||
self.tau_ = np.empty(self.N,dtype=float)
|
||||
self.v_ = np.empty(self.N,dtype=float)
|
||||
self.tau_ = np.empty(self.num_data,dtype=float)
|
||||
self.v_ = np.empty(self.num_data,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)
|
||||
z = np.empty(self.num_data,dtype=float)
|
||||
self.Z_hat = np.empty(self.num_data,dtype=float)
|
||||
phi = np.empty(self.num_data,dtype=float)
|
||||
mu_hat = np.empty(self.num_data,dtype=float)
|
||||
sigma2_hat = np.empty(self.num_data,dtype=float)
|
||||
|
||||
#Approximation
|
||||
epsilon_np1 = self.epsilon + 1.
|
||||
|
|
@ -119,7 +128,7 @@ 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]
|
||||
|
|
@ -137,23 +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_np2 = sum((self.v_tilde-self.np2[-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.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!
|
||||
|
|
@ -182,7 +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()
|
||||
|
||||
|
|
@ -192,15 +210,15 @@ class EP(likelihood):
|
|||
sigma_ = 1./tau_
|
||||
mu_ = v_/tau_
|
||||
"""
|
||||
self.tau_ = np.empty(self.N,dtype=float)
|
||||
self.v_ = np.empty(self.N,dtype=float)
|
||||
self.tau_ = np.empty(self.num_data,dtype=float)
|
||||
self.v_ = np.empty(self.num_data,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)
|
||||
z = np.empty(self.num_data,dtype=float)
|
||||
self.Z_hat = np.empty(self.num_data,dtype=float)
|
||||
phi = np.empty(self.num_data,dtype=float)
|
||||
mu_hat = np.empty(self.num_data,dtype=float)
|
||||
sigma2_hat = np.empty(self.num_data,dtype=float)
|
||||
|
||||
#Approximation
|
||||
epsilon_np1 = 1
|
||||
|
|
@ -209,7 +227,7 @@ 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]
|
||||
|
|
@ -238,18 +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_np2 = sum((self.v_tilde-np2[-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.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]
|
||||
|
||||
"""
|
||||
|
|
@ -272,9 +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()
|
||||
|
|
@ -287,15 +313,15 @@ class EP(likelihood):
|
|||
sigma_ = 1./tau_
|
||||
mu_ = v_/tau_
|
||||
"""
|
||||
self.tau_ = np.empty(self.N,dtype=float)
|
||||
self.v_ = np.empty(self.N,dtype=float)
|
||||
self.tau_ = np.empty(self.num_data,dtype=float)
|
||||
self.v_ = np.empty(self.num_data,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)
|
||||
z = np.empty(self.num_data,dtype=float)
|
||||
self.Z_hat = np.empty(self.num_data,dtype=float)
|
||||
phi = np.empty(self.num_data,dtype=float)
|
||||
mu_hat = np.empty(self.num_data,dtype=float)
|
||||
sigma2_hat = np.empty(self.num_data,dtype=float)
|
||||
|
||||
#Approximation
|
||||
epsilon_np1 = 1
|
||||
|
|
@ -304,7 +330,7 @@ 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]
|
||||
|
|
@ -343,8 +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_np2 = sum((self.v_tilde-self.np2[-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.num_data
|
||||
self.np1.append(self.tau_tilde.copy())
|
||||
self.np2.append(self.v_tilde.copy())
|
||||
|
||||
|
|
|
|||
|
|
@ -10,14 +10,16 @@ class likelihood(Parameterized):
|
|||
(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.covariance_matrix : the effective (noise) covariance of the GP targets
|
||||
self.Z : a factor which gets added to the likelihood (0 for a Gaussian, Z_EP for EP)
|
||||
self.is_heteroscedastic : enables significant computational savings in GP
|
||||
self.precision : a scalar or vector representation of the effective target precision
|
||||
self.YYT : (optional) = np.dot(self.Y, self.Y.T) enables computational savings for D>N
|
||||
self.V : self.precision * self.Y
|
||||
|
||||
- self.Y : the effective Gaussian target of the GP
|
||||
- self.N, self.D : Y.shape
|
||||
- self.covariance_matrix : the effective (noise) covariance of the GP targets
|
||||
- self.Z : a factor which gets added to the likelihood (0 for a Gaussian, Z_EP for EP)
|
||||
- self.is_heteroscedastic : enables significant computational savings in GP
|
||||
- self.precision : a scalar or vector representation of the effective target precision
|
||||
- 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):
|
||||
Parameterized.__init__(self)
|
||||
|
|
|
|||
|
|
@ -1,6 +1,7 @@
|
|||
# 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
|
||||
|
|
@ -116,18 +117,3 @@ class Binomial(NoiseDistribution):
|
|||
|
||||
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
|
||||
|
||||
"""
|
||||
def predictive_values(self,mu,var): #TODO remove
|
||||
mu = mu.flatten()
|
||||
var = var.flatten()
|
||||
#mean = stats.norm.cdf(mu/np.sqrt(1+var))
|
||||
mean = self._predictive_mean_analytical(mu,np.sqrt(var))
|
||||
norm_025 = [stats.norm.ppf(.025,m,v) for m,v in zip(mu,var)]
|
||||
norm_975 = [stats.norm.ppf(.975,m,v) for m,v in zip(mu,var)]
|
||||
#p_025 = stats.norm.cdf(norm_025/np.sqrt(1+var))
|
||||
#p_975 = stats.norm.cdf(norm_975/np.sqrt(1+var))
|
||||
p_025 = self._predictive_mean_analytical(norm_025,np.sqrt(var))
|
||||
p_975 = self._predictive_mean_analytical(norm_975,np.sqrt(var))
|
||||
return mean[:,None], np.nan*var, p_025[:,None], p_975[:,None] # TODO: var
|
||||
"""
|
||||
|
|
|
|||
|
|
@ -11,7 +11,7 @@ from noise_distributions import NoiseDistribution
|
|||
|
||||
class Exponential(NoiseDistribution):
|
||||
"""
|
||||
Gamma likelihood
|
||||
Expoential likelihood
|
||||
Y is expected to take values in {0,1,2,...}
|
||||
-----
|
||||
$$
|
||||
|
|
|
|||
|
|
@ -57,12 +57,12 @@ class Gaussian(NoiseDistribution):
|
|||
new_sigma2 = self.predictive_variance(mu,sigma)
|
||||
return new_sigma2*(mu/sigma**2 + self.gp_link.transf(mu)/self.variance)
|
||||
|
||||
def _predictive_variance_analytical(self,mu,sigma,*args): #TODO *args?
|
||||
def _predictive_variance_analytical(self,mu,sigma):
|
||||
return 1./(1./self.variance + 1./sigma**2)
|
||||
|
||||
def _mass(self,gp,obs):
|
||||
#return std_norm_pdf( (self.gp_link.transf(gp)-obs)/np.sqrt(self.variance) )
|
||||
return stats.norm.pdf(obs,self.gp_link.transf(gp),np.sqrt(self.variance)) #FIXME
|
||||
return stats.norm.pdf(obs,self.gp_link.transf(gp),np.sqrt(self.variance))
|
||||
|
||||
def _nlog_mass(self,gp,obs):
|
||||
return .5*((self.gp_link.transf(gp)-obs)**2/self.variance + np.log(2.*np.pi*self.variance))
|
||||
|
|
|
|||
|
|
@ -13,20 +13,38 @@ class GPTransformation(object):
|
|||
Link function class for doing non-Gaussian likelihoods approximation
|
||||
|
||||
:param Y: observed output (Nx1 numpy.darray)
|
||||
..Note:: Y values allowed depend on the likelihood_function used
|
||||
|
||||
.. note:: Y values allowed depend on the likelihood_function used
|
||||
|
||||
"""
|
||||
def __init__(self):
|
||||
pass
|
||||
|
||||
def transf(self,f):
|
||||
"""
|
||||
Gaussian process tranformation function, latent space -> output space
|
||||
"""
|
||||
pass
|
||||
|
||||
def dtransf_df(self,f):
|
||||
"""
|
||||
derivative of transf(f) w.r.t. f
|
||||
"""
|
||||
pass
|
||||
|
||||
def d2transf_df2(self,f):
|
||||
"""
|
||||
second derivative of transf(f) w.r.t. f
|
||||
"""
|
||||
pass
|
||||
|
||||
class Identity(GPTransformation):
|
||||
"""
|
||||
$$
|
||||
g(f) = f
|
||||
$$
|
||||
"""
|
||||
#def transf(self,mu):
|
||||
# return mu
|
||||
.. math::
|
||||
|
||||
g(f) = f
|
||||
|
||||
"""
|
||||
def transf(self,f):
|
||||
return f
|
||||
|
||||
|
|
@ -39,13 +57,11 @@ class Identity(GPTransformation):
|
|||
|
||||
class Probit(GPTransformation):
|
||||
"""
|
||||
$$
|
||||
g(f) = \\Phi^{-1} (mu)
|
||||
$$
|
||||
"""
|
||||
#def transf(self,mu):
|
||||
# return inv_std_norm_cdf(mu)
|
||||
.. math::
|
||||
|
||||
g(f) = \\Phi^{-1} (mu)
|
||||
|
||||
"""
|
||||
def transf(self,f):
|
||||
return std_norm_cdf(f)
|
||||
|
||||
|
|
@ -57,13 +73,11 @@ class Probit(GPTransformation):
|
|||
|
||||
class Log(GPTransformation):
|
||||
"""
|
||||
$$
|
||||
g(f) = \log(\mu)
|
||||
$$
|
||||
"""
|
||||
#def transf(self,mu):
|
||||
# return np.log(mu)
|
||||
.. math::
|
||||
|
||||
g(f) = \\log(\\mu)
|
||||
|
||||
"""
|
||||
def transf(self,f):
|
||||
return np.exp(f)
|
||||
|
||||
|
|
@ -75,20 +89,12 @@ class Log(GPTransformation):
|
|||
|
||||
class Log_ex_1(GPTransformation):
|
||||
"""
|
||||
$$
|
||||
g(f) = \log(\exp(\mu) - 1)
|
||||
$$
|
||||
"""
|
||||
#def transf(self,mu):
|
||||
# """
|
||||
# function: output space -> latent space
|
||||
# """
|
||||
# return np.log(np.exp(mu) - 1)
|
||||
.. math::
|
||||
|
||||
g(f) = \\log(\\exp(\\mu) - 1)
|
||||
|
||||
"""
|
||||
def transf(self,f):
|
||||
"""
|
||||
function: latent space -> output space
|
||||
"""
|
||||
return np.log(1.+np.exp(f))
|
||||
|
||||
def dtransf_df(self,f):
|
||||
|
|
@ -110,9 +116,11 @@ class Reciprocal(GPTransformation):
|
|||
|
||||
class Heaviside(GPTransformation):
|
||||
"""
|
||||
$$
|
||||
g(f) = I_{x \in A}
|
||||
$$
|
||||
|
||||
.. math::
|
||||
|
||||
g(f) = I_{x \\in A}
|
||||
|
||||
"""
|
||||
def transf(self,f):
|
||||
#transformation goes here
|
||||
|
|
|
|||
|
|
@ -16,10 +16,11 @@ 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
|
||||
|
||||
.. 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."#FIXME
|
||||
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
|
||||
|
|
@ -50,7 +51,9 @@ class NoiseDistribution(object):
|
|||
"""
|
||||
In case it is needed, this function assess the output values or makes any pertinent transformation on them.
|
||||
|
||||
:param Y: observed output (Nx1 numpy.darray)
|
||||
:param Y: observed output
|
||||
:type Y: Nx1 numpy.darray
|
||||
|
||||
"""
|
||||
return Y
|
||||
|
||||
|
|
@ -62,18 +65,21 @@ class NoiseDistribution(object):
|
|||
: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.
|
||||
|
||||
.. 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)
|
||||
|
||||
|
|
@ -85,6 +91,7 @@ class NoiseDistribution(object):
|
|||
: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)
|
||||
|
||||
|
|
@ -96,6 +103,7 @@ class NoiseDistribution(object):
|
|||
: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)
|
||||
|
||||
|
|
@ -106,6 +114,7 @@ class NoiseDistribution(object):
|
|||
: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)
|
||||
|
||||
|
|
@ -122,6 +131,7 @@ class NoiseDistribution(object):
|
|||
: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))
|
||||
|
|
@ -137,7 +147,8 @@ class NoiseDistribution(object):
|
|||
: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))
|
||||
.. 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))
|
||||
|
||||
|
|
@ -148,6 +159,7 @@ class NoiseDistribution(object):
|
|||
: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)
|
||||
|
||||
|
|
@ -158,6 +170,7 @@ class NoiseDistribution(object):
|
|||
: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
|
||||
|
||||
|
|
@ -169,7 +182,8 @@ class NoiseDistribution(object):
|
|||
:param mu: cavity distribution mean
|
||||
:param sigma: cavity distribution standard deviation
|
||||
|
||||
..Note:: This function helps computing E(V(Y_star|f_star))
|
||||
.. note:: This function helps computing E(V(Y_star|f_star))
|
||||
|
||||
"""
|
||||
return .5*((gp - mu)/sigma)**2 - np.log(self._variance(gp))
|
||||
|
||||
|
|
@ -180,6 +194,7 @@ class NoiseDistribution(object):
|
|||
: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)
|
||||
|
||||
|
|
@ -190,6 +205,7 @@ class NoiseDistribution(object):
|
|||
: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
|
||||
|
||||
|
|
@ -201,7 +217,8 @@ class NoiseDistribution(object):
|
|||
:param mu: cavity distribution mean
|
||||
:param sigma: cavity distribution standard deviation
|
||||
|
||||
..Note:: This function helps computing E( E(Y_star|f_star)**2 )
|
||||
.. note:: This function helps computing E( E(Y_star|f_star)**2 )
|
||||
|
||||
"""
|
||||
return .5*((gp - mu)/sigma)**2 - 2*np.log(self._mean(gp))
|
||||
|
||||
|
|
@ -212,6 +229,7 @@ class NoiseDistribution(object):
|
|||
: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)
|
||||
|
||||
|
|
@ -222,6 +240,7 @@ class NoiseDistribution(object):
|
|||
: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 )
|
||||
|
||||
|
|
@ -243,6 +262,7 @@ class NoiseDistribution(object):
|
|||
|
||||
: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)
|
||||
|
|
@ -266,6 +286,7 @@ class NoiseDistribution(object):
|
|||
|
||||
: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)
|
||||
|
|
@ -278,6 +299,7 @@ class NoiseDistribution(object):
|
|||
: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)
|
||||
|
|
@ -310,6 +332,7 @@ class NoiseDistribution(object):
|
|||
: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)
|
||||
|
|
@ -321,6 +344,7 @@ class NoiseDistribution(object):
|
|||
: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)
|
||||
|
||||
|
|
@ -331,7 +355,9 @@ class NoiseDistribution(object):
|
|||
:param x: tuple (latent variable,output)
|
||||
:param mu: latent variable's predictive mean
|
||||
:param sigma: latent variable's predictive standard deviation
|
||||
..Note: Only avilable when the output is continuous
|
||||
|
||||
.. 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])))
|
||||
|
|
@ -343,7 +369,9 @@ class NoiseDistribution(object):
|
|||
:param x: tuple (latent variable,output)
|
||||
:param mu: latent variable's predictive mean
|
||||
:param sigma: latent variable's predictive standard deviation
|
||||
..Note: Only avilable when the output is continuous
|
||||
|
||||
.. 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])
|
||||
|
|
@ -356,14 +384,17 @@ class NoiseDistribution(object):
|
|||
: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
|
||||
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]
|
||||
|
|
|
|||
|
|
@ -12,29 +12,22 @@ from noise_distributions import NoiseDistribution
|
|||
class Poisson(NoiseDistribution):
|
||||
"""
|
||||
Poisson likelihood
|
||||
Y is expected to take values in {0,1,2,...}
|
||||
-----
|
||||
$$
|
||||
L(x) = \exp(\lambda) * \lambda**Y_i / Y_i!
|
||||
$$
|
||||
|
||||
.. 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):
|
||||
#self.discrete = True
|
||||
#self.support_limits = (0,np.inf)
|
||||
|
||||
#self.analytical_mean = False
|
||||
super(Poisson, self).__init__(gp_link,analytical_mean,analytical_variance)
|
||||
|
||||
def _preprocess_values(self,Y): #TODO
|
||||
#self.scale = .5*Y.max()
|
||||
#self.shift = Y.mean()
|
||||
return Y #(Y - self.shift)/self.scale
|
||||
return Y
|
||||
|
||||
def _mass(self,gp,obs):
|
||||
"""
|
||||
Mass (or density) function
|
||||
"""
|
||||
#obs = obs*self.scale + self.shift
|
||||
return stats.poisson.pmf(obs,self.gp_link.transf(gp))
|
||||
|
||||
def _nlog_mass(self,gp,obs):
|
||||
|
|
@ -51,15 +44,6 @@ class Poisson(NoiseDistribution):
|
|||
transf = self.gp_link.transf(gp)
|
||||
return obs * ((self.gp_link.dtransf_df(gp)/transf)**2 - d2_df/transf) + d2_df
|
||||
|
||||
def _dnlog_mass_dobs(self,obs,gp): #TODO not needed
|
||||
return special.psi(obs+1) - np.log(self.gp_link.transf(gp))
|
||||
|
||||
def _d2nlog_mass_dobs2(self,obs,gp=None): #TODO not needed
|
||||
return special.polygamma(1,obs)
|
||||
|
||||
def _d2nlog_mass_dcross(self,obs,gp): #TODO not needed
|
||||
return -self.gp_link.dtransf_df(gp)/self.gp_link.transf(gp)
|
||||
|
||||
def _mean(self,gp):
|
||||
"""
|
||||
Mass (or density) function
|
||||
|
|
|
|||
|
|
@ -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):
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
@ -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 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 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 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:
|
||||
|
|
|
|||
|
|
@ -25,14 +25,14 @@ class GPMultioutputRegression(GP):
|
|||
: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 W_columns: number tuples of the corregionalization parameters 'coregion_W' (see coregionalize kernel documentation)
|
||||
:type W_columns: integer
|
||||
: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,W_columns=1):
|
||||
def __init__(self,X_list,Y_list,kernel_list=None,noise_variance_list=None,normalize_X=False,normalize_Y=False,rank=1):
|
||||
|
||||
self.num_outputs = len(Y_list)
|
||||
assert len(X_list) == self.num_outputs, 'Number of outputs do not match length of inputs list.'
|
||||
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
|
||||
|
|
@ -51,7 +51,7 @@ class GPMultioutputRegression(GP):
|
|||
#Coregionalization kernel definition
|
||||
if kernel_list is None:
|
||||
kernel_list = [kern.rbf(original_dim)]
|
||||
mkernel = kern.build_lcm(input_dim=original_dim, num_outputs=self.num_outputs, kernel_list = kernel_list, W_columns=W_columns)
|
||||
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)
|
||||
|
|
|
|||
|
|
@ -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',
|
||||
|
|
@ -338,8 +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]
|
||||
|
|
|
|||
|
|
@ -30,23 +30,23 @@ class SparseGPMultioutputRegression(SparseGP):
|
|||
: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 W_columns: number tuples of the corregionalization parameters 'coregion_W' (see coregionalize kernel documentation)
|
||||
:type W_columns: 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,W_columns=1):
|
||||
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.num_outputs = len(Y_list)
|
||||
assert len(X_list) == self.num_outputs, 'Number of outputs do not match length of inputs list.'
|
||||
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.num_outputs, 'Number of outputs do not match length of inducing inputs 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.num_outputs
|
||||
num_inducing = [num_inducing] * self.output_dim
|
||||
num_inducing = np.asarray(num_inducing)
|
||||
assert num_inducing.size == self.num_outputs, 'Number of outputs do not match length of inducing inputs list.'
|
||||
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())
|
||||
|
|
@ -72,7 +72,7 @@ class SparseGPMultioutputRegression(SparseGP):
|
|||
#Coregionalization kernel definition
|
||||
if kernel_list is None:
|
||||
kernel_list = [kern.rbf(original_dim)]
|
||||
mkernel = kern.build_lcm(input_dim=original_dim, num_outputs=self.num_outputs, kernel_list = kernel_list, W_columns=W_columns)
|
||||
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)
|
||||
|
|
|
|||
50
GPy/testing/bcgplvm_tests.py
Normal file
50
GPy/testing/bcgplvm_tests.py
Normal file
|
|
@ -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()
|
||||
|
|
@ -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)
|
||||
|
|
|
|||
|
|
@ -21,6 +21,10 @@ class KernelTests(unittest.TestCase):
|
|||
kern = GPy.kern.rbf(5)
|
||||
self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
|
||||
|
||||
def test_rbf_sympykernel(self):
|
||||
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))
|
||||
|
|
@ -79,19 +83,19 @@ class KernelTests(unittest.TestCase):
|
|||
kern = GPy.kern.poly(5, degree=4)
|
||||
self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
|
||||
|
||||
def test_coregionalization(self):
|
||||
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.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 + 2.
|
||||
Y = np.vstack((Y1,Y2))
|
||||
# def test_coregionalization(self):
|
||||
# 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.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 + 2.
|
||||
# Y = np.vstack((Y1,Y2))
|
||||
|
||||
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))
|
||||
# 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__":
|
||||
|
|
|
|||
|
|
@ -105,7 +105,7 @@ class Test(unittest.TestCase):
|
|||
|
||||
def test_psi2(self):
|
||||
for kern in self.kerns:
|
||||
Nsamples = self.Nsamples/300.
|
||||
Nsamples = self.Nsamples/10.
|
||||
psi2 = kern.psi2(self.Z, self.q_x_mean, self.q_x_variance)
|
||||
K_ = np.zeros((self.num_inducing, self.num_inducing))
|
||||
diffs = []
|
||||
|
|
|
|||
|
|
@ -238,6 +238,18 @@ class GradientTests(unittest.TestCase):
|
|||
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..."
|
||||
|
|
|
|||
|
|
@ -7,9 +7,21 @@ import urllib as url
|
|||
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),
|
||||
|
|
@ -130,14 +142,18 @@ The database was created with funding from NSF EIA-0196217.""",
|
|||
'license' : None,
|
||||
'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 = raw_input().lower()
|
||||
choice = ''
|
||||
if ipython_notebook:
|
||||
ipynb_input(choice, prompt='provide your answer here')
|
||||
else:
|
||||
choice = raw_input().lower()
|
||||
if choice in yes:
|
||||
return True
|
||||
elif choice in no:
|
||||
|
|
@ -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
|
||||
|
|
|
|||
63
GPy/util/erfcx.py
Normal file
63
GPy/util/erfcx.py
Normal file
|
|
@ -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)
|
||||
|
||||
|
|
@ -27,48 +27,56 @@ 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: A inverse
|
||||
|
||||
"""
|
||||
return lapack.dpotri(A, lower=lower)
|
||||
|
||||
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]
|
||||
|
|
@ -115,14 +123,16 @@ 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)
|
||||
|
|
@ -142,6 +152,7 @@ def jitchol_old(A, maxtries=5):
|
|||
|
||||
def pdinv(A, *args):
|
||||
"""
|
||||
|
||||
:param A: A DxD pd numpy array
|
||||
|
||||
:rval Ai: the inverse of A
|
||||
|
|
@ -152,6 +163,7 @@ 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)))
|
||||
|
|
@ -177,14 +189,13 @@ def chol_inv(L):
|
|||
|
||||
def multiple_pdinv(A):
|
||||
"""
|
||||
Arguments
|
||||
---------
|
||||
:param A: A DxDxN numpy array (each A[:,:,i] is pd)
|
||||
|
||||
Returns
|
||||
-------
|
||||
invs : the inverses of A
|
||||
hld: 0.5* the log of the determinants of A
|
||||
:rval invs: the inverses of A
|
||||
:rtype invs: np.ndarray
|
||||
:rval 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)]
|
||||
|
|
@ -198,15 +209,13 @@ 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)"
|
||||
|
|
@ -273,11 +282,10 @@ 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])
|
||||
|
|
@ -295,11 +303,10 @@ 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, :])
|
||||
|
||||
|
|
@ -363,8 +370,9 @@ 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_
|
||||
where L_ is the lower chol of K + x*x^T
|
||||
if L is the lower chol. of K, then this function computes L\_
|
||||
where L\_ is the lower chol of K + x*x^T
|
||||
|
||||
"""
|
||||
support_code = """
|
||||
#include <math.h>
|
||||
|
|
|
|||
110
GPy/util/ln_diff_erfs.py
Normal file
110
GPy/util/ln_diff_erfs.py
Normal file
|
|
@ -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
|
||||
|
|
@ -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:
|
||||
|
||||
D: dimension of the grid
|
||||
n: number of points
|
||||
min_max: (min, max) list
|
||||
|
||||
:param D: dimension of the grid
|
||||
:param n: number of points
|
||||
:param 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
|
||||
|
|
|
|||
|
|
@ -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.
|
||||
ARG j : the index of the second vertex to be swapped.
|
||||
RETURN tree : the tree structure with the two vertex locations
|
||||
swapped.
|
||||
|
||||
:param tree: the tree for which two vertices are to be swapped.
|
||||
:param i: the index of the first vertex to be swapped.
|
||||
:param j: the index of the second vertex to be 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.
|
||||
ARG zangle : rotation for z-axis.
|
||||
ARG order : the order for the rotations."""
|
||||
|
||||
:param xangle: rotation for x-axis.
|
||||
:param yangle: rotation for y-axis.
|
||||
: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.
|
||||
ARG file_name : the file name to load in.
|
||||
RETURN skel : the skeleton for the file."""
|
||||
"""
|
||||
Loads an ASF file into a skeleton structure.
|
||||
|
||||
:param file_name: The file name to load in.
|
||||
|
||||
"""
|
||||
|
||||
fid = open(file_name, 'r')
|
||||
self.read_skel(fid)
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
32
GPy/util/symbolic.py
Normal file
32
GPy/util/symbolic.py
Normal file
|
|
@ -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
|
||||
|
|
@ -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.
|
||||
|
||||
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)
|
||||
.. 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)
|
||||
|
||||
"""
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -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 ==
|
||||
iterations: number of N.R. iterations
|
||||
:param 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 ==
|
||||
iterations: number of N.R. iterations
|
||||
:param max_iterations: maximum 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
|
||||
|
||||
"""
|
||||
|
||||
|
|
|
|||
|
|
@ -2,7 +2,7 @@
|
|||
#
|
||||
|
||||
# You can set these variables from the command line.
|
||||
SPHINXOPTS =
|
||||
SPHINXOPTS = -a -w log.txt -E
|
||||
SPHINXBUILD = sphinx-build
|
||||
PAPER =
|
||||
BUILDDIR = _build
|
||||
|
|
|
|||
|
|
@ -106,7 +106,7 @@ class Mock(object):
|
|||
print "Mocking"
|
||||
MOCK_MODULES = ['sympy',
|
||||
'sympy.utilities', 'sympy.utilities.codegen', 'sympy.core.cache',
|
||||
'sympy.core', 'sympy.parsing', 'sympy.parsing.sympy_parser'
|
||||
'sympy.core', 'sympy.parsing', 'sympy.parsing.sympy_parser', 'Tango', 'numdifftools'
|
||||
]
|
||||
for mod_name in MOCK_MODULES:
|
||||
sys.modules[mod_name] = Mock()
|
||||
|
|
|
|||
|
|
@ -20,7 +20,7 @@ All of the examples included in GPy return an instance
|
|||
of a model class, and therefore they can be called in
|
||||
the following way: ::
|
||||
|
||||
import numpy as np
|
||||
import numpy as np
|
||||
import pylab as pb
|
||||
pb.ion()
|
||||
import GPy
|
||||
|
|
@ -107,7 +107,7 @@ inputs: ::
|
|||
m['iip'] = np.arange(-5,0)
|
||||
|
||||
Getting the model's likelihood and gradients
|
||||
===========================================
|
||||
=============================================
|
||||
Appart form the printing the model, the marginal
|
||||
log-likelihood can be obtained by using the function
|
||||
``log_likelihood()``. Also, the log-likelihood gradients
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue