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einsumming in rbf for speed
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James Hensman
parent
d5658660a6
commit
c87bda9e49
1 changed files with 63 additions and 52 deletions
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@ -70,34 +70,39 @@ class RBF(Stationary):
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self.lengthscale.gradient += (dL_dpsi2[:,:,:,None] * _dpsi2_dlengthscale).reshape(-1,self.input_dim).sum(axis=0)
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self.lengthscale.gradient += (dL_dpsi2[:,:,:,None] * _dpsi2_dlengthscale).reshape(-1,self.input_dim).sum(axis=0)
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return
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return
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l2 = self.lengthscale **2
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elif isinstance(variational_posterior, variational.NormalPosterior):
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l2 = self.lengthscale **2
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#contributions from psi0:
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#contributions from psi0:
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self.variance.gradient = np.sum(dL_dpsi0)
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self.variance.gradient = np.sum(dL_dpsi0)
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self.lengthscale.gradient = 0.
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self.lengthscale.gradient = 0.
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#from psi1
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denom, _, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
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d_length = psi1[:,:,None] * ((dist_sq - 1.)/(self.lengthscale*denom) +1./self.lengthscale)
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dpsi1_dlength = d_length * dL_dpsi1[:, :, None]
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if self.ARD:
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self.lengthscale.gradient += dpsi1_dlength.sum(0).sum(0)
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else:
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self.lengthscale.gradient += dpsi1_dlength.sum()
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self.variance.gradient += np.sum(dL_dpsi1 * psi1) / self.variance
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#from psi2
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S = variational_posterior.variance
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_, Zdist_sq, _, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
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d_length = 2.*psi2[:, :, :, None] * (Zdist_sq * (2.*S[:,None,None,:]/l2 + 1.) + mudist_sq + S[:, None, None, :] / l2) / (2.*S[:,None,None,:] + l2)*self.lengthscale
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dpsi2_dlength = d_length * dL_dpsi2[:, :, :, None]
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if not self.ARD:
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self.lengthscale.gradient += dpsi2_dlength.sum()
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else:
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self.lengthscale.gradient += dpsi2_dlength.sum(0).sum(0).sum(0)
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self.variance.gradient += 2.*np.sum(dL_dpsi2 * psi2)/self.variance
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#from psi1
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denom, _, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
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d_length = psi1[:,:,None] * ((dist_sq - 1.)/(self.lengthscale*denom) +1./self.lengthscale)
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dpsi1_dlength = d_length * dL_dpsi1[:, :, None]
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if self.ARD:
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self.lengthscale.gradient += dpsi1_dlength.sum(0).sum(0)
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else:
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else:
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self.lengthscale.gradient += dpsi1_dlength.sum()
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raise ValueError, "unknown distriubtion received for psi-statistics"
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self.variance.gradient += np.sum(dL_dpsi1 * psi1) / self.variance
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#from psi2
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S = variational_posterior.variance
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_, Zdist_sq, _, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
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d_length = 2.*psi2[:, :, :, None] * (Zdist_sq * (2.*S[:,None,None,:]/l2 + 1.) + mudist_sq + S[:, None, None, :] / l2) / (2.*S[:,None,None,:] + l2)*self.lengthscale
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dpsi2_dlength = d_length * dL_dpsi2[:, :, :, None]
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if not self.ARD:
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self.lengthscale.gradient += dpsi2_dlength.sum()
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else:
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self.lengthscale.gradient += dpsi2_dlength.sum(0).sum(0).sum(0)
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self.variance.gradient += 2.*np.sum(dL_dpsi2 * psi2)/self.variance
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def gradients_Z_expectations(self, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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def gradients_Z_expectations(self, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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# Spike-and-Slab GPLVM
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# Spike-and-Slab GPLVM
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@ -112,25 +117,26 @@ class RBF(Stationary):
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grad += (dL_dpsi2[:, :, :, None] * _dpsi2_dZ).sum(axis=0).sum(axis=1)
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grad += (dL_dpsi2[:, :, :, None] * _dpsi2_dZ).sum(axis=0).sum(axis=1)
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return grad
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return grad
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l2 = self.lengthscale **2
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#psi1
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elif isinstance(variational_posterior, variational.NormalPosterior):
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denom, dist, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
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denominator = l2 * denom
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l2 = self.lengthscale **2
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dpsi1_dZ = -psi1[:, :, None] * (dist / denominator)
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grad = np.sum(dL_dpsi1[:, :, None] * dpsi1_dZ, 0)
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#psi2
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#psi1
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Zdist, Zdist_sq, mudist, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
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denom, dist, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
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term1 = Zdist / l2 # M, M, Q
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grad = np.einsum('ij,ij,ijk,ijk->jk', dL_dpsi1, psi1, dist, -1./(denom*l2))
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S = variational_posterior.variance
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term2 = mudist / (2.*S[:,None,None,:] + l2) # N, M, M, Q
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dZ = psi2[:, :, :, None] * (term1[None, :, :, :] + term2) #N,M,M,Q
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#psi2
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grad += 2*(dL_dpsi2[:, :, :, None] * dZ).sum(0).sum(0)
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Zdist, Zdist_sq, mudist, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
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term1 = Zdist / l2 # M, M, Q
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S = variational_posterior.variance
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term2 = mudist / (2.*S[:,None,None,:] + l2) # N, M, M, Q
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return grad
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grad += 2.*np.einsum('ijk,ijk,ijkl->kl', dL_dpsi2, psi2, term1[None,:,:,:] + term2)
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return grad
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else:
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raise ValueError, "unknown distriubtion received for psi-statistics"
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def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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# Spike-and-Slab GPLVM
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# Spike-and-Slab GPLVM
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@ -150,19 +156,24 @@ class RBF(Stationary):
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grad_gamma += (dL_dpsi2[:,:,:, None] * _dpsi2_dgamma).reshape(ndata,-1,self.input_dim).sum(axis=1)
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grad_gamma += (dL_dpsi2[:,:,:, None] * _dpsi2_dgamma).reshape(ndata,-1,self.input_dim).sum(axis=1)
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return grad_mu, grad_S, grad_gamma
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return grad_mu, grad_S, grad_gamma
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elif isinstance(variational_posterior, variational.NormalPosterior):
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l2 = self.lengthscale **2
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l2 = self.lengthscale **2
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#psi1
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#psi1
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denom, dist, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
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denom, dist, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
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tmp = psi1[:, :, None] / l2 / denom
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tmp = psi1[:, :, None] / l2 / denom
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grad_mu = np.sum(dL_dpsi1[:, :, None] * tmp * dist, 1)
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grad_mu = np.sum(dL_dpsi1[:, :, None] * tmp * dist, 1)
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grad_S = np.sum(dL_dpsi1[:, :, None] * 0.5 * tmp * (dist_sq - 1), 1)
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grad_S = np.sum(dL_dpsi1[:, :, None] * 0.5 * tmp * (dist_sq - 1), 1)
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#psi2
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#psi2
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_, _, mudist, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
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_, _, mudist, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
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S = variational_posterior.variance
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S = variational_posterior.variance
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tmp = psi2[:, :, :, None] / (2.*S[:,None,None,:] + l2)
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tmp = psi2[:, :, :, None] / (2.*S[:,None,None,:] + l2)
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grad_mu += -2.*(dL_dpsi2[:, :, :, None] * tmp * mudist).sum(1).sum(1)
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grad_mu += -2.*np.einsum('ijk,ijkl,ijkl->il', dL_dpsi2, tmp , mudist)
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grad_S += (dL_dpsi2[:, :, :, None] * tmp * (2.*mudist_sq - 1)).sum(1).sum(1)
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grad_S += np.einsum('ijk,ijkl,ijkl->il', dL_dpsi2 , tmp , (2.*mudist_sq - 1))
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else:
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raise ValueError, "unknown distriubtion received for psi-statistics"
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return grad_mu, grad_S
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return grad_mu, grad_S
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