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[SSGPLVM] implemented linear kernel
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Zhenwen Dai
parent
16555aa11d
commit
99d6b8220c
6 changed files with 147 additions and 34 deletions
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@ -6,10 +6,12 @@ import numpy as np
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from scipy import weave
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from kern import Kern
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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 ...util.misc import param_to_array
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from ...core.parameterization import Param
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from ...core.parameterization.transformations import Logexp
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from ...util.caching import Cache_this
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from ...core.parameterization import variational
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from psi_comp import linear_psi_comp
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class Linear(Kern):
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"""
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@ -104,49 +106,109 @@ class Linear(Kern):
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#---------------------------------------#
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def psi0(self, Z, variational_posterior):
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return np.sum(self.variances * self._mu2S(variational_posterior), 1)
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if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
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gamma = variational_posterior.binary_prob
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mu = variational_posterior.mean
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S = variational_posterior.variance
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return np.einsum('q,nq,nq->n',self.variances,gamma,np.square(mu)+S)
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# return (self.variances*gamma*(np.square(mu)+S)).sum(axis=1)
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else:
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return np.sum(self.variances * self._mu2S(variational_posterior), 1)
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def psi1(self, Z, variational_posterior):
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return self.K(variational_posterior.mean, Z) #the variance, it does nothing
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if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
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gamma = variational_posterior.binary_prob
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mu = variational_posterior.mean
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return np.einsum('nq,q,mq,nq->nm',gamma,self.variances,Z,mu)
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# return (self.variances*gamma*mu).sum(axis=1)
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else:
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return self.K(variational_posterior.mean, Z) #the variance, it does nothing
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@Cache_this(limit=1)
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def psi2(self, Z, variational_posterior):
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ZA = Z * self.variances
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ZAinner = self._ZAinner(variational_posterior, Z)
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return np.dot(ZAinner, ZA.T)
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if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
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gamma = variational_posterior.binary_prob
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mu = variational_posterior.mean
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S = variational_posterior.variance
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mu2 = np.square(mu)
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variances2 = np.square(self.variances)
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tmp = np.einsum('nq,q,mq,nq->nm',gamma,self.variances,Z,mu)
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return np.einsum('nq,q,mq,oq,nq->nmo',gamma,variances2,Z,Z,mu2+S)+\
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np.einsum('nm,no->nmo',tmp,tmp) - np.einsum('nq,q,mq,oq,nq->nmo',np.square(gamma),variances2,Z,Z,mu2)
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else:
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ZA = Z * self.variances
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ZAinner = self._ZAinner(variational_posterior, Z)
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return np.dot(ZAinner, ZA.T)
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def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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#psi1
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self.update_gradients_full(dL_dpsi1, variational_posterior.mean, Z)
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# psi0:
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tmp = dL_dpsi0[:, None] * self._mu2S(variational_posterior)
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if self.ARD: self.variances.gradient += tmp.sum(0)
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else: self.variances.gradient += tmp.sum()
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#psi2
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if self.ARD:
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tmp = dL_dpsi2[:, :, :, None] * (self._ZAinner(variational_posterior, Z)[:, :, None, :] * Z[None, None, :, :])
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self.variances.gradient += 2.*tmp.sum(0).sum(0).sum(0)
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if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
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gamma = variational_posterior.binary_prob
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mu = variational_posterior.mean
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S = variational_posterior.variance
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mu2S = np.square(mu)+S
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_dpsi2_dvariance, _, _, _, _ = linear_psi_comp._psi2computations(self.variances, Z, mu, S, gamma)
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grad = np.einsum('n,nq,nq->q',dL_dpsi0,gamma,mu2S) + np.einsum('nm,nq,mq,nq->q',dL_dpsi1,gamma,Z,mu) +\
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np.einsum('nmo,nmoq->q',dL_dpsi2,_dpsi2_dvariance)
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self.variances.gradient = grad
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else:
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self.variances.gradient += 2.*np.sum(dL_dpsi2 * self.psi2(Z, variational_posterior))/self.variances
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#psi1
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self.update_gradients_full(dL_dpsi1, variational_posterior.mean, Z)
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# psi0:
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tmp = dL_dpsi0[:, None] * self._mu2S(variational_posterior)
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if self.ARD: self.variances.gradient += tmp.sum(0)
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else: self.variances.gradient += tmp.sum()
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#psi2
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if self.ARD:
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tmp = dL_dpsi2[:, :, :, None] * (self._ZAinner(variational_posterior, Z)[:, :, None, :] * Z[None, None, :, :])
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self.variances.gradient += 2.*tmp.sum(0).sum(0).sum(0)
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else:
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self.variances.gradient += 2.*np.sum(dL_dpsi2 * self.psi2(Z, variational_posterior))/self.variances
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def gradients_Z_expectations(self, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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#psi1
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grad = self.gradients_X(dL_dpsi1.T, Z, variational_posterior.mean)
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#psi2
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self._weave_dpsi2_dZ(dL_dpsi2, Z, variational_posterior, grad)
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return grad
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if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
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gamma = variational_posterior.binary_prob
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mu = variational_posterior.mean
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S = variational_posterior.variance
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_, _, _, _, _dpsi2_dZ = linear_psi_comp._psi2computations(self.variances, Z, mu, S, gamma)
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grad = np.einsum('nm,nq,q,nq->mq',dL_dpsi1,gamma, self.variances,mu) +\
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np.einsum('nmo,noq->mq',dL_dpsi2,_dpsi2_dZ)
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return grad
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else:
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#psi1
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grad = self.gradients_X(dL_dpsi1.T, Z, variational_posterior.mean)
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#psi2
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self._weave_dpsi2_dZ(dL_dpsi2, Z, variational_posterior, grad)
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return grad
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def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
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grad_mu, grad_S = np.zeros(variational_posterior.mean.shape), np.zeros(variational_posterior.mean.shape)
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# psi0
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grad_mu += dL_dpsi0[:, None] * (2.0 * variational_posterior.mean * self.variances)
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grad_S += dL_dpsi0[:, None] * self.variances
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# psi1
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grad_mu += (dL_dpsi1[:, :, None] * (Z * self.variances)).sum(1)
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# psi2
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self._weave_dpsi2_dmuS(dL_dpsi2, Z, variational_posterior, grad_mu, grad_S)
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return grad_mu, grad_S
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if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
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gamma = variational_posterior.binary_prob
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mu = variational_posterior.mean
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S = variational_posterior.variance
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mu2S = np.square(mu)+S
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_, _dpsi2_dgamma, _dpsi2_dmu, _dpsi2_dS, _ = linear_psi_comp._psi2computations(self.variances, Z, mu, S, gamma)
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grad_gamma = np.einsum('n,q,nq->nq',dL_dpsi0,self.variances,mu2S) + np.einsum('nm,q,mq,nq->nq',dL_dpsi1,self.variances,Z,mu) +\
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np.einsum('nmo,nmoq->nq',dL_dpsi2,_dpsi2_dgamma)
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grad_mu = np.einsum('n,nq,q,nq->nq',dL_dpsi0,gamma,2.*self.variances,mu) + np.einsum('nm,nq,q,mq->nq',dL_dpsi1,gamma,self.variances,Z) +\
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np.einsum('nmo,nmoq->nq',dL_dpsi2,_dpsi2_dmu)
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grad_S = np.einsum('n,nq,q->nq',dL_dpsi0,gamma,self.variances) + np.einsum('nmo,nmoq->nq',dL_dpsi2,_dpsi2_dS)
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return grad_mu, grad_S, grad_gamma
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else:
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grad_mu, grad_S = np.zeros(variational_posterior.mean.shape), np.zeros(variational_posterior.mean.shape)
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# psi0
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grad_mu += dL_dpsi0[:, None] * (2.0 * variational_posterior.mean * self.variances)
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grad_S += dL_dpsi0[:, None] * self.variances
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# psi1
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grad_mu += (dL_dpsi1[:, :, None] * (Z * self.variances)).sum(1)
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# psi2
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self._weave_dpsi2_dmuS(dL_dpsi2, Z, variational_posterior, grad_mu, grad_S)
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return grad_mu, grad_S
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#--------------------------------------------------#
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# Helpers for psi statistics #
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51
GPy/kern/_src/psi_comp/linear_psi_comp.py
Normal file
51
GPy/kern/_src/psi_comp/linear_psi_comp.py
Normal file
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@ -0,0 +1,51 @@
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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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"""
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The package for the Psi statistics computation of the linear kernel for SSGPLVM
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"""
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import numpy as np
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from GPy.util.caching import Cache_this
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#@Cache_this(limit=1)
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def _psi2computations(variance, Z, mu, S, gamma):
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"""
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Z - MxQ
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mu - NxQ
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S - NxQ
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gamma - NxQ
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"""
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# here are the "statistics" for psi1 and psi2
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# Produced intermediate results:
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# _psi2 NxMxM
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# _psi2_dvariance NxMxMxQ
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# _psi2_dZ NxMxQ
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# _psi2_dgamma NxMxMxQ
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# _psi2_dmu NxMxMxQ
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# _psi2_dS NxMxMxQ
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mu2 = np.square(mu)
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gamma2 = np.square(gamma)
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variance2 = np.square(variance)
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mu2S = mu2+S # NxQ
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common_sum = np.einsum('nq,q,mq,nq->nm',gamma,variance,Z,mu) # NxM
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_dpsi2_dvariance = np.einsum('nq,q,mq,oq->nmoq',2.*(gamma*mu2S-gamma2*mu2),variance,Z,Z)+\
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np.einsum('nq,mq,nq,no->nmoq',gamma,Z,mu,common_sum)+\
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np.einsum('nq,oq,nq,nm->nmoq',gamma,Z,mu,common_sum)
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_dpsi2_dgamma = np.einsum('q,mq,oq,nq->nmoq',variance2,Z,Z,(mu2S-2.*gamma*mu2))+\
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np.einsum('q,mq,nq,no->nmoq',variance,Z,mu,common_sum)+\
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np.einsum('q,oq,nq,nm->nmoq',variance,Z,mu,common_sum)
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_dpsi2_dmu = np.einsum('q,mq,oq,nq,nq->nmoq',variance2,Z,Z,mu,2.*(gamma-gamma2))+\
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np.einsum('nq,q,mq,no->nmoq',gamma,variance,Z,common_sum)+\
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np.einsum('nq,q,oq,nm->nmoq',gamma,variance,Z,common_sum)
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_dpsi2_dS = np.einsum('nq,q,mq,oq->nmoq',gamma,variance2,Z,Z)
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_dpsi2_dZ = 2.*(np.einsum('nq,q,mq,nq->nmq',gamma,variance2,Z,mu2S)+np.einsum('nq,q,nq,nm->nmq',gamma,variance,mu,common_sum)
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-np.einsum('nq,q,mq,nq->nmq',gamma2,variance2,Z,mu2))
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return _dpsi2_dvariance, _dpsi2_dgamma, _dpsi2_dmu, _dpsi2_dS, _dpsi2_dZ
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@ -8,7 +8,7 @@ from ...util.misc import param_to_array
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from stationary import Stationary
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from GPy.util.caching import Cache_this
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from ...core.parameterization import variational
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from rbf_psi_comp import ssrbf_psi_comp
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from psi_comp import ssrbf_psi_comp
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class RBF(Stationary):
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"""
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@ -7,7 +7,7 @@ import numpy as np
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from ...util.linalg import tdot
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from ...util.config import *
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from stationary import Stationary
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from rbf_psi_comp import ssrbf_psi_comp
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from psi_comp import ssrbf_psi_comp
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class SSRBF(Stationary):
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"""
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