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https://github.com/SheffieldML/GPy.git
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adapt the new interface of the variational posterior distribution.
This commit is contained in:
Zhenwen Dai
parent
34d9f90d92
commit
99c6a2095f
7 changed files with 96 additions and 389 deletions
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@ -29,3 +29,29 @@ class Normal(Parameterized):
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assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
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from ...plotting.matplot_dep import variational_plots
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return variational_plots.plot(self,*args)
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class SpikeAndSlab(Parameterized):
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'''
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The SpikeAndSlab distribution for variational approximations.
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'''
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def __init__(self, means, variances, binary_prob, name='latent space'):
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"""
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binary_prob : the probability of the distribution on the slab part.
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"""
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Parameterized.__init__(self, name=name)
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self.mean = Param("mean", means)
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self.variance = Param('variance', variances, Logexp())
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self.gamma = Param("binary_prob",binary_prob,)
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self.add_parameters(self.mean, self.variance, self.gamma)
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def plot(self, *args):
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"""
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Plot latent space X in 1D:
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See GPy.plotting.matplot_dep.variational_plots
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"""
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import sys
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assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
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from ...plotting.matplot_dep import variational_plots
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return variational_plots.plot(self,*args)
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@ -57,11 +57,14 @@ class SparseGP(GP):
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return not (self.X_variance is None)
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def parameters_changed(self):
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self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.X_variance, self.Z, self.likelihood, self.Y)
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if self.has_uncertain_inputs():
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self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference_latent(self.kern, self.q, self.Z, self.likelihood, self.Y)
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else:
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self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.X_variance, self.Z, self.likelihood, self.Y)
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self.likelihood.update_gradients(self.grad_dict.pop('partial_for_likelihood'))
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if self.has_uncertain_inputs():
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self.kern.update_gradients_variational(mu=self.X, S=self.X_variance, Z=self.Z, **self.grad_dict)
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self.Z.gradient = self.kern.gradients_Z_variational(mu=self.X, S=self.X_variance, Z=self.Z, **self.grad_dict)
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self.kern.update_gradients_variational(posterior_variational=self.q, Z=self.Z, **self.grad_dict)
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self.Z.gradient = self.kern.gradients_Z_variational(posterior_variational=self.q, Z=self.Z, **self.grad_dict)
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else:
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self.kern.update_gradients_sparse(X=self.X, Z=self.Z, **self.grad_dict)
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self.Z.gradient = self.kern.gradients_Z_sparse(X=self.X, Z=self.Z, **self.grad_dict)
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@ -43,9 +43,20 @@ class VarDTC(object):
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return Y * prec # TODO chache this, and make it effective
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def inference(self, kern, X, X_variance, Z, likelihood, Y):
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"""Inference for normal sparseGP"""
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uncertain_inputs = False
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psi0, psi1, psi2 = _compute_psi(kern, X, X_variance, Z, uncertain_inputs)
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return self._inference(kern, psi0, psi1, psi2, Z, likelihood, Y, uncertain_inputs)
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def inference_latent(self, kern, posterior_variational, Z, likelihood, Y):
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"""Inference for GPLVM with uncertain inputs"""
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uncertain_inputs = True
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psi0, psi1, psi2 = _compute_psi_latent(kern, posterior_variational, Z)
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return self._inference(kern, psi0, psi1, psi2, Z, likelihood, Y, uncertain_inputs)
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def _inference(self, kern, psi0, psi1, psi2, Z, likelihood, Y, uncertain_inputs):
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#see whether we're using variational uncertain inputs
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uncertain_inputs = not (X_variance is None)
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_, output_dim = Y.shape
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@ -62,10 +73,9 @@ class VarDTC(object):
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# do the inference:
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het_noise = beta.size < 1
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num_inducing = Z.shape[0]
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num_data = X.shape[0]
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num_data = Y.shape[0]
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# kernel computations, using BGPLVM notation
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Kmm = kern.K(Z)
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psi0, psi1, psi2 = _compute_psi(kern, X, X_variance, Z, uncertain_inputs)
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Kmm = kern.K(Z)
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Lm = jitchol(Kmm)
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@ -191,20 +201,31 @@ class VarDTCMissingData(object):
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else:
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self._subarray_indices = [[slice(None),slice(None)]]
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return [Y], [(Y**2).sum()]
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def inference(self, kern, X, X_variance, Z, likelihood, Y):
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"""Inference for normal sparseGP"""
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uncertain_inputs = False
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psi0, psi1, psi2 = _compute_psi(kern, X, X_variance, Z, uncertain_inputs)
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return self._inference(kern, psi0, psi1, psi2, Z, likelihood, Y, uncertain_inputs)
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def inference_latent(self, kern, posterior_variational, Z, likelihood, Y):
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"""Inference for GPLVM with uncertain inputs"""
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uncertain_inputs = True
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psi0, psi1, psi2 = _compute_psi_latent(kern, posterior_variational, Z)
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return self._inference(kern, psi0, psi1, psi2, Z, likelihood, Y, uncertain_inputs)
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def _inference(self, kern, psi0_all, psi1_all, psi2_all, Z, likelihood, Y, uncertain_inputs):
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Ys, traces = self._Y(Y)
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beta_all = 1./likelihood.variance
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uncertain_inputs = not (X_variance is None)
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het_noise = beta_all.size != 1
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import itertools
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num_inducing = Z.shape[0]
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dL_dpsi0_all = np.zeros(X.shape[0])
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dL_dpsi1_all = np.zeros((X.shape[0], num_inducing))
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dL_dpsi0_all = np.zeros(Y.shape[0])
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dL_dpsi1_all = np.zeros((Y.shape[0], num_inducing))
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if uncertain_inputs:
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dL_dpsi2_all = np.zeros((X.shape[0], num_inducing, num_inducing))
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dL_dpsi2_all = np.zeros((Y.shape[0], num_inducing, num_inducing))
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partial_for_likelihood = 0
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woodbury_vector = np.zeros((num_inducing, Y.shape[1]))
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@ -217,9 +238,6 @@ class VarDTCMissingData(object):
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Lm = jitchol(Kmm)
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if uncertain_inputs: LmInv = dtrtri(Lm)
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# kernel computations, using BGPLVM notation
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psi0_all, psi1_all, psi2_all = _compute_psi(kern, X, X_variance, Z, uncertain_inputs)
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VVT_factor_all = np.empty(Y.shape)
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full_VVT_factor = VVT_factor_all.shape[1] == Y.shape[1]
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if not full_VVT_factor:
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@ -340,15 +358,16 @@ class VarDTCMissingData(object):
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return post, log_marginal, grad_dict
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def _compute_psi(kern, X, X_variance, Z, uncertain_inputs):
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if uncertain_inputs:
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psi0 = kern.psi0(Z, X, X_variance)
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psi1 = kern.psi1(Z, X, X_variance)
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psi2 = kern.psi2(Z, X, X_variance)
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else:
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psi0 = kern.Kdiag(X)
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psi1 = kern.K(X, Z)
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psi2 = None
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def _compute_psi(kern, X, X_variance, Z):
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psi0 = kern.Kdiag(X)
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psi1 = kern.K(X, Z)
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psi2 = None
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return psi0, psi1, psi2
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def _compute_psi_latent(kern, posterior_variational, Z):
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psi0 = kern.psi0(Z, posterior_variational)
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psi1 = kern.psi1(Z, posterior_variational)
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psi2 = kern.psi2(Z, posterior_variational)
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return psi0, psi1, psi2
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def _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm, VVT_factor, Cpsi1Vf, DBi_plus_BiPBi, psi1, het_noise, uncertain_inputs):
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@ -26,11 +26,11 @@ class Kern(Parameterized):
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raise NotImplementedError
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def Kdiag(self, Xa):
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raise NotImplementedError
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def psi0(self,Z,mu,S):
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def psi0(self,Z,posterior_variational):
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raise NotImplementedError
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def psi1(self,Z,mu,S):
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def psi1(self,Z,posterior_variational):
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raise NotImplementedError
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def psi2(self,Z,mu,S):
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def psi2(self,Z,posterior_variational):
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raise NotImplementedError
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def gradients_X(self, dL_dK, X, X2):
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raise NotImplementedError
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@ -49,16 +49,16 @@ class Kern(Parameterized):
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self._collect_gradient(target)
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self._set_gradient(target)
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def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, posterior_variational):
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"""Set the gradients of all parameters when doing variational (M) inference with uncertain inputs."""
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raise NotImplementedError
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def gradients_Z_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z):
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grad = self.gradients_X(dL_dKmm, Z)
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grad += self.gradients_X(dL_dKnm.T, Z, X)
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return grad
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def gradients_Z_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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def gradients_Z_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, posterior_variational):
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raise NotImplementedError
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def gradients_muS_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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def gradients_q_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, posterior_variational):
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raise NotImplementedError
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def plot_ARD(self, *args):
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@ -79,16 +79,21 @@ class RBF(Kern):
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ret[:] = self.variance
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return ret
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def psi0(self, Z, mu, S):
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def psi0(self, Z, posterior_variational):
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mu = posterior_variational.mean
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ret = np.empty(mu.shape[0], dtype=np.float64)
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ret[:] = self.variance
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return ret
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def psi1(self, Z, mu, S):
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def psi1(self, Z, posterior_variational):
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mu = posterior_variational.mean
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S = posterior_variational.variance
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self._psi_computations(Z, mu, S)
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return self._psi1
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def psi2(self, Z, mu, S):
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def psi2(self, Z, posterior_variational):
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mu = posterior_variational.mean
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S = posterior_variational.variance
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self._psi_computations(Z, mu, S)
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return self._psi2
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@ -121,7 +126,9 @@ class RBF(Kern):
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else:
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self.lengthscale.gradient += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dKmm)
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def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, posterior_variational):
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mu = posterior_variational.mean
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S = posterior_variational.variance
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self._psi_computations(Z, mu, S)
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#contributions from psi0:
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@ -155,7 +162,9 @@ class RBF(Kern):
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else:
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self.lengthscale.gradient += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dKmm)
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def gradients_Z_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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def gradients_Z_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, posterior_variational):
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mu = posterior_variational.mean
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S = posterior_variational.variance
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self._psi_computations(Z, mu, S)
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#psi1
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@ -173,7 +182,9 @@ class RBF(Kern):
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return grad
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def gradients_muS_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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def gradients_q_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, posterior_variational):
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mu = posterior_variational.mean
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S = posterior_variational.variance
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self._psi_computations(Z, mu, S)
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#psi1
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tmp = self._psi1[:, :, None] / self.lengthscale2 / self._psi1_denom
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@ -1,352 +0,0 @@
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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from kernpart import Kernpart
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from ...util.linalg import tdot
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from ...util.misc import fast_array_equal, param_to_array
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from ...core.parameterization import Param
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class SS_RBF(Kernpart):
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"""
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The RBF kernel for Spike-and-Slab GPLVM
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Radial Basis Function kernel, aka squared-exponential, exponentiated quadratic or Gaussian kernel:
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.. math::
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k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg) \ \ \ \ \ \\text{ where } r^2 = \sum_{i=1}^d \\frac{ (x_i-x^\prime_i)^2}{\ell_i^2}
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where \ell_i is the lengthscale, \sigma^2 the variance and d the dimensionality of the input.
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:param input_dim: the number of input dimensions
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:type input_dim: int
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:param variance: the variance of the kernel
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:type variance: float
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:param lengthscale: the vector of lengthscale of the kernel
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:type lengthscale: array or list of the appropriate size (or float if there is only one lengthscale parameter)
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:rtype: kernel object
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"""
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def __init__(self, input_dim, variance=1., lengthscale=None, name='rbf'):
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super(RBF, self).__init__(input_dim, name)
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self.input_dim = input_dim
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if lengthscale is not None:
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lengthscale = np.asarray(lengthscale)
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assert lengthscale.size == self.input_dim, "bad number of lengthscales"
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else:
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lengthscale = np.ones(self.input_dim)
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self.variance = Param('variance', variance)
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self.lengthscale = Param('lengthscale', lengthscale)
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self.lengthscale.add_observer(self, self.update_lengthscale)
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self.add_parameters(self.variance, self.lengthscale)
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self.parameters_changed() # initializes cache
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def on_input_change(self, X):
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#self._K_computations(X, None)
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pass
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def update_lengthscale(self, l):
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self.lengthscale2 = np.square(self.lengthscale)
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def parameters_changed(self):
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# reset cached results
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self._X, self._X2 = np.empty(shape=(2, 1))
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self._Z, self._mu, self._S = np.empty(shape=(3, 1)) # cached versions of Z,mu,S
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def K(self, X, X2, target):
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self._K_computations(X, X2)
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target += self.variance * self._K_dvar
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def Kdiag(self, X, target):
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np.add(target, self.variance, target)
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def psi0(self, Z, mu, S, target):
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target += self.variance
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def psi1(self, Z, mu, S, target):
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self._psi_computations(Z, mu, S)
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target += self._psi1
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def psi2(self, Z, mu, S, target):
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self._psi_computations(Z, mu, S)
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target += self._psi2
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def update_gradients_full(self, dL_dK, X):
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self._K_computations(X, None)
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self.variance.gradient = np.sum(self._K_dvar * dL_dK)
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if self.ARD:
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self.lengthscale.gradient = self._dL_dlengthscales_via_K(dL_dK, X, None)
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else:
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self.lengthscale.gradient = (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dK)
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def update_gradients_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z):
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#contributions from Kdiag
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self.variance.gradient = np.sum(dL_dKdiag)
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#from Knm
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self._K_computations(X, Z)
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self.variance.gradient += np.sum(dL_dKnm * self._K_dvar)
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if self.ARD:
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self.lengthscales.gradient = self._dL_dlengthscales_via_K(dL_dKnm, X, Z)
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else:
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self.lengthscale.gradient = (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dKmm)
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#from Kmm
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self._K_computations(Z, None)
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self.variance.gradient += np.sum(dL_dKmm * self._K_dvar)
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if self.ARD:
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self.lengthscales.gradient += self._dL_dlengthscales_via_K(dL_dKmm, Z, None)
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else:
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self.lengthscale.gradient += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dKmm)
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def update_gradients_variational(self, dL_dKmm, dL_dpsi0, dL_dpsi1, dL_dpsi2, mu, S, Z):
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self._psi_computations(Z, mu, S)
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#contributions from psi0:
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self.variance.gradient = np.sum(dL_dpsi0)
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#from psi1
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self.variance.gradient += np.sum(dL_dpsi1 * self._psi1 / self.variance)
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d_length = self._psi1[:,:,None] * ((self._psi1_dist_sq - 1.)/(self.lengthscale*self._psi1_denom) +1./self.lengthscale)
|
||||
dpsi1_dlength = d_length * dL_dpsi1[:, :, None]
|
||||
if not self.ARD:
|
||||
self.lengthscale.gradeint = dpsi1_dlength.sum()
|
||||
else:
|
||||
self.lengthscale.gradient = dpsi1_dlength.sum(0).sum(0)
|
||||
|
||||
#from psi2
|
||||
d_var = 2.*self._psi2 / self.variance
|
||||
d_length = 2.*self._psi2[:, :, :, None] * (self._psi2_Zdist_sq * self._psi2_denom + self._psi2_mudist_sq + S[:, None, None, :] / self.lengthscale2) / (self.lengthscale * self._psi2_denom)
|
||||
|
||||
self.variance.gradient += np.sum(dL_dpsi2 * d_var)
|
||||
dpsi2_dlength = d_length * dL_dpsi2[:, :, :, None]
|
||||
if not self.ARD:
|
||||
self.lengthscale.gradient += dpsi2_dlength.sum()
|
||||
else:
|
||||
self.lengthscale.gradient += dpsi2_dlength.sum(0).sum(0).sum(0)
|
||||
|
||||
#from Kmm
|
||||
self._K_computations(Z, None)
|
||||
self.variance.gradient += np.sum(dL_dKmm * self._K_dvar)
|
||||
if self.ARD:
|
||||
self.lengthscales.gradient += self._dL_dlengthscales_via_K(dL_dKmm, Z, None)
|
||||
else:
|
||||
self.lengthscale.gradient += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dK)
|
||||
|
||||
def gradients_X(self, dL_dK, X, X2, target):
|
||||
#if self._X is None or X.base is not self._X.base or X2 is not None:
|
||||
self._K_computations(X, X2)
|
||||
if X2 is None:
|
||||
_K_dist = 2*(X[:, None, :] - X[None, :, :])
|
||||
else:
|
||||
_K_dist = X[:, None, :] - X2[None, :, :] # don't cache this in _K_computations because it is high memory. If this function is being called, chances are we're not in the high memory arena.
|
||||
gradients_X = (-self.variance / self.lengthscale2) * np.transpose(self._K_dvar[:, :, np.newaxis] * _K_dist, (1, 0, 2))
|
||||
target += np.sum(gradients_X * dL_dK.T[:, :, None], 0)
|
||||
|
||||
def dKdiag_dX(self, dL_dKdiag, X, target):
|
||||
pass
|
||||
|
||||
#---------------------------------------#
|
||||
# PSI statistics #
|
||||
#---------------------------------------#
|
||||
|
||||
def dpsi0_dmuS(self, dL_dpsi0, Z, mu, S, target_mu, target_S):
|
||||
pass
|
||||
|
||||
def dpsi1_dZ(self, dL_dpsi1, Z, mu, S, target):
|
||||
self._psi_computations(Z, mu, S)
|
||||
denominator = (self.lengthscale2 * (self._psi1_denom))
|
||||
dpsi1_dZ = -self._psi1[:, :, None] * ((self._psi1_dist / denominator))
|
||||
target += np.sum(dL_dpsi1[:, :, None] * dpsi1_dZ, 0)
|
||||
|
||||
def dpsi1_dmuS(self, dL_dpsi1, Z, mu, S, target_mu, target_S):
|
||||
self._psi_computations(Z, mu, S)
|
||||
tmp = self._psi1[:, :, None] / self.lengthscale2 / self._psi1_denom
|
||||
target_mu += np.sum(dL_dpsi1[:, :, None] * tmp * self._psi1_dist, 1)
|
||||
target_S += np.sum(dL_dpsi1[:, :, None] * 0.5 * tmp * (self._psi1_dist_sq - 1), 1)
|
||||
|
||||
def dpsi2_dZ(self, dL_dpsi2, Z, mu, S, target):
|
||||
self._psi_computations(Z, mu, S)
|
||||
term1 = self._psi2_Zdist / self.lengthscale2 # num_inducing, num_inducing, input_dim
|
||||
term2 = self._psi2_mudist / self._psi2_denom / self.lengthscale2 # N, num_inducing, num_inducing, input_dim
|
||||
dZ = self._psi2[:, :, :, None] * (term1[None] + term2)
|
||||
target += (dL_dpsi2[:, :, :, None] * dZ).sum(0).sum(0)
|
||||
|
||||
def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S, target_mu, target_S):
|
||||
"""Think N,num_inducing,num_inducing,input_dim """
|
||||
self._psi_computations(Z, mu, S)
|
||||
tmp = self._psi2[:, :, :, None] / self.lengthscale2 / self._psi2_denom
|
||||
target_mu += -2.*(dL_dpsi2[:, :, :, None] * tmp * self._psi2_mudist).sum(1).sum(1)
|
||||
target_S += (dL_dpsi2[:, :, :, None] * tmp * (2.*self._psi2_mudist_sq - 1)).sum(1).sum(1)
|
||||
|
||||
#---------------------------------------#
|
||||
# Precomputations #
|
||||
#---------------------------------------#
|
||||
|
||||
def _K_computations(self, X, X2):
|
||||
#params = self._get_params()
|
||||
if not (fast_array_equal(X, self._X) and fast_array_equal(X2, self._X2)):# and fast_array_equal(self._params_save , params)):
|
||||
#self._X = X.copy()
|
||||
#self._params_save = params.copy()
|
||||
if X2 is None:
|
||||
self._X2 = None
|
||||
X = X / self.lengthscale
|
||||
Xsquare = np.sum(np.square(X), 1)
|
||||
self._K_dist2 = -2.*tdot(X) + (Xsquare[:, None] + Xsquare[None, :])
|
||||
else:
|
||||
self._X2 = X2.copy()
|
||||
X = X / self.lengthscale
|
||||
X2 = X2 / self.lengthscale
|
||||
self._K_dist2 = -2.*np.dot(X, X2.T) + (np.sum(np.square(X), 1)[:, None] + np.sum(np.square(X2), 1)[None, :])
|
||||
self._K_dvar = np.exp(-0.5 * self._K_dist2)
|
||||
|
||||
def _dL_dlengthscales_via_K(self, dL_dK, X, X2):
|
||||
"""
|
||||
A helper function for update_gradients_* methods
|
||||
|
||||
Computes the derivative of the objective L wrt the lengthscales via
|
||||
|
||||
dL_dl = sum_{i,j}(dL_dK_{ij} dK_dl)
|
||||
|
||||
assumes self._K_computations has just been called.
|
||||
|
||||
This is only valid if self.ARD=True
|
||||
"""
|
||||
target = np.zeros(self.input_dim)
|
||||
dvardLdK = self._K_dvar * dL_dK
|
||||
var_len3 = self.variance / np.power(self.lengthscale, 3)
|
||||
if X2 is None:
|
||||
# save computation for the symmetrical case
|
||||
dvardLdK = dvardLdK + dvardLdK.T
|
||||
code = """
|
||||
int q,i,j;
|
||||
double tmp;
|
||||
for(q=0; q<input_dim; q++){
|
||||
tmp = 0;
|
||||
for(i=0; i<num_data; i++){
|
||||
for(j=0; j<i; j++){
|
||||
tmp += (X(i,q)-X(j,q))*(X(i,q)-X(j,q))*dvardLdK(i,j);
|
||||
}
|
||||
}
|
||||
target(q) += var_len3(q)*tmp;
|
||||
}
|
||||
"""
|
||||
num_data, num_inducing, input_dim = X.shape[0], X.shape[0], self.input_dim
|
||||
X, dvardLdK = param_to_array(X, dvardLdK)
|
||||
weave.inline(code, arg_names=['num_data', 'num_inducing', 'input_dim', 'X', 'target', 'dvardLdK', 'var_len3'], type_converters=weave.converters.blitz, **self.weave_options)
|
||||
else:
|
||||
code = """
|
||||
int q,i,j;
|
||||
double tmp;
|
||||
for(q=0; q<input_dim; q++){
|
||||
tmp = 0;
|
||||
for(i=0; i<num_data; i++){
|
||||
for(j=0; j<num_inducing; j++){
|
||||
tmp += (X(i,q)-X2(j,q))*(X(i,q)-X2(j,q))*dvardLdK(i,j);
|
||||
}
|
||||
}
|
||||
target(q) += var_len3(q)*tmp;
|
||||
}
|
||||
"""
|
||||
num_data, num_inducing, input_dim = X.shape[0], X2.shape[0], self.input_dim
|
||||
X, X2, dvardLdK = param_to_array(X, X2, dvardLdK)
|
||||
weave.inline(code, arg_names=['num_data', 'num_inducing', 'input_dim', 'X', 'X2', 'target', 'dvardLdK', 'var_len3'], type_converters=weave.converters.blitz, **self.weave_options)
|
||||
return target
|
||||
|
||||
|
||||
|
||||
def _psi_computations(self, Z, mu, S):
|
||||
# here are the "statistics" for psi1 and psi2
|
||||
Z_changed = not fast_array_equal(Z, self._Z)
|
||||
if Z_changed:
|
||||
# Z has changed, compute Z specific stuff
|
||||
self._psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
|
||||
self._psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
|
||||
self._psi2_Zdist_sq = np.square(self._psi2_Zdist / self.lengthscale) # M,M,Q
|
||||
|
||||
if Z_changed or not fast_array_equal(mu, self._mu) or not fast_array_equal(S, self._S):
|
||||
# something's changed. recompute EVERYTHING
|
||||
|
||||
# psi1
|
||||
self._psi1_denom = S[:, None, :] / self.lengthscale2 + 1.
|
||||
self._psi1_dist = Z[None, :, :] - mu[:, None, :]
|
||||
self._psi1_dist_sq = np.square(self._psi1_dist) / self.lengthscale2 / self._psi1_denom
|
||||
self._psi1_exponent = -0.5 * np.sum(self._psi1_dist_sq + np.log(self._psi1_denom), -1)
|
||||
self._psi1 = self.variance * np.exp(self._psi1_exponent)
|
||||
|
||||
# psi2
|
||||
self._psi2_denom = 2.*S[:, None, None, :] / self.lengthscale2 + 1. # N,M,M,Q
|
||||
self._psi2_mudist, self._psi2_mudist_sq, self._psi2_exponent, _ = self.weave_psi2(mu, self._psi2_Zhat)
|
||||
# self._psi2_mudist = mu[:,None,None,:]-self._psi2_Zhat #N,M,M,Q
|
||||
# self._psi2_mudist_sq = np.square(self._psi2_mudist)/(self.lengthscale2*self._psi2_denom)
|
||||
# self._psi2_exponent = np.sum(-self._psi2_Zdist_sq -self._psi2_mudist_sq -0.5*np.log(self._psi2_denom),-1) #N,M,M,Q
|
||||
self._psi2 = np.square(self.variance) * np.exp(self._psi2_exponent) # N,M,M,Q
|
||||
|
||||
# store matrices for caching
|
||||
self._Z, self._mu, self._S = Z, mu, S
|
||||
|
||||
def weave_psi2(self, mu, Zhat):
|
||||
N, input_dim = mu.shape
|
||||
num_inducing = Zhat.shape[0]
|
||||
|
||||
mudist = np.empty((N, num_inducing, num_inducing, input_dim))
|
||||
mudist_sq = np.empty((N, num_inducing, num_inducing, input_dim))
|
||||
psi2_exponent = np.zeros((N, num_inducing, num_inducing))
|
||||
psi2 = np.empty((N, num_inducing, num_inducing))
|
||||
|
||||
psi2_Zdist_sq = self._psi2_Zdist_sq
|
||||
_psi2_denom = self._psi2_denom.squeeze().reshape(N, self.input_dim)
|
||||
half_log_psi2_denom = 0.5 * np.log(self._psi2_denom).squeeze().reshape(N, self.input_dim)
|
||||
variance_sq = float(np.square(self.variance))
|
||||
if self.ARD:
|
||||
lengthscale2 = self.lengthscale2
|
||||
else:
|
||||
lengthscale2 = np.ones(input_dim) * self.lengthscale2
|
||||
code = """
|
||||
double tmp;
|
||||
|
||||
#pragma omp parallel for private(tmp)
|
||||
for (int n=0; n<N; n++){
|
||||
for (int m=0; m<num_inducing; m++){
|
||||
for (int mm=0; mm<(m+1); mm++){
|
||||
for (int q=0; q<input_dim; q++){
|
||||
//compute mudist
|
||||
tmp = mu(n,q) - Zhat(m,mm,q);
|
||||
mudist(n,m,mm,q) = tmp;
|
||||
mudist(n,mm,m,q) = tmp;
|
||||
|
||||
//now mudist_sq
|
||||
tmp = tmp*tmp/lengthscale2(q)/_psi2_denom(n,q);
|
||||
mudist_sq(n,m,mm,q) = tmp;
|
||||
mudist_sq(n,mm,m,q) = tmp;
|
||||
|
||||
//now psi2_exponent
|
||||
tmp = -psi2_Zdist_sq(m,mm,q) - tmp - half_log_psi2_denom(n,q);
|
||||
psi2_exponent(n,mm,m) += tmp;
|
||||
if (m !=mm){
|
||||
psi2_exponent(n,m,mm) += tmp;
|
||||
}
|
||||
//psi2 would be computed like this, but np is faster
|
||||
//tmp = variance_sq*exp(psi2_exponent(n,m,mm));
|
||||
//psi2(n,m,mm) = tmp;
|
||||
//psi2(n,mm,m) = tmp;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
"""
|
||||
|
||||
support_code = """
|
||||
#include <omp.h>
|
||||
#include <math.h>
|
||||
"""
|
||||
weave.inline(code, support_code=support_code, libraries=['gomp'],
|
||||
arg_names=['N', 'num_inducing', 'input_dim', 'mu', 'Zhat', 'mudist_sq', 'mudist', 'lengthscale2', '_psi2_denom', 'psi2_Zdist_sq', 'psi2_exponent', 'half_log_psi2_denom', 'psi2', 'variance_sq'],
|
||||
type_converters=weave.converters.blitz, **self.weave_options)
|
||||
|
||||
return mudist, mudist_sq, psi2_exponent, psi2
|
||||
|
|
@ -66,7 +66,7 @@ class BayesianGPLVM(SparseGP, GPLVM):
|
|||
super(BayesianGPLVM, self).parameters_changed()
|
||||
|
||||
self._log_marginal_likelihood -= self.KL_divergence()
|
||||
dL_dmu, dL_dS = self.kern.gradients_muS_variational(mu=self.X, S=self.X_variance, Z=self.Z, **self.grad_dict)
|
||||
dL_dmu, dL_dS = self.kern.gradients_q_variational(posterior_variational=self.q, Z=self.Z, **self.grad_dict)
|
||||
|
||||
# dL:
|
||||
self.q.mean.gradient = dL_dmu
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue