rename sslinear_psi_comp.py

GPy/kern/_src/psi_comp/sslinear_psi_comp.py

@@ -0,0 +1,88 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+"""
+The package for the Psi statistics computation of the linear kernel for SSGPLVM
+"""
+
+import numpy as np
+
+def psicomputations(variance, Z, variational_posterior):
+    """
+    Compute psi-statistics for ss-linear kernel
+    """
+    # here are the "statistics" for psi0, psi1 and psi2
+    # Produced intermediate results:
+    # psi0    N
+    # psi1    NxM
+    # psi2    MxM
+    mu = variational_posterior.mean
+    S = variational_posterior.variance
+    gamma = variational_posterior.binary_prob
+
+    psi0 = np.einsum('q,nq,nq->n',variance,gamma,np.square(mu)+S)
+    psi1 = np.einsum('nq,q,mq,nq->nm',gamma,variance,Z,mu)
+    mu2 = np.square(mu)
+    variances2 = np.square(variance)
+    tmp = np.einsum('nq,q,mq,nq->nm',gamma,variance,Z,mu)
+    psi2 = np.einsum('nq,q,mq,oq,nq->mo',gamma,variances2,Z,Z,mu2+S)+\
+           np.einsum('nm,no->mo',tmp,tmp) - np.einsum('nq,q,mq,oq,nq->mo',np.square(gamma),variances2,Z,Z,mu2)
+
+    return psi0, psi1, psi2
+
+def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, Z, variational_posterior):
+    mu = variational_posterior.mean
+    S = variational_posterior.variance
+    gamma = variational_posterior.binary_prob
+
+    dL_dvar, dL_dgamma, dL_dmu, dL_dS, dL_dZ = _psi2computations(dL_dpsi2, variance, Z, mu, S, gamma)
+
+    # Compute for psi0 and psi1
+    mu2S = np.square(mu)+S
+    dL_dvar += np.einsum('n,nq,nq->q',dL_dpsi0,gamma,mu2S) + np.einsum('nm,nq,mq,nq->q',dL_dpsi1,gamma,Z,mu)
+    dL_dgamma += np.einsum('n,q,nq->nq',dL_dpsi0,variance,mu2S) + np.einsum('nm,q,mq,nq->nq',dL_dpsi1,variance,Z,mu)
+    dL_dmu += np.einsum('n,nq,q,nq->nq',dL_dpsi0,gamma,2.*variance,mu) + np.einsum('nm,nq,q,mq->nq',dL_dpsi1,gamma,variance,Z)
+    dL_dS += np.einsum('n,nq,q->nq',dL_dpsi0,gamma,variance)
+    dL_dZ +=  np.einsum('nm,nq,q,nq->mq',dL_dpsi1,gamma, variance,mu)
+    
+    return dL_dvar, dL_dZ, dL_dmu, dL_dS, dL_dgamma
+
+def _psi2computations(dL_dpsi2, variance, Z, mu, S, gamma):
+    """
+    Z - MxQ
+    mu - NxQ
+    S - NxQ
+    gamma - NxQ
+    """
+    # here are the "statistics" for psi1 and psi2
+    # Produced intermediate results:
+    # _psi2_dvariance      Q
+    # _psi2_dZ             MxQ
+    # _psi2_dgamma         NxQ
+    # _psi2_dmu            NxQ
+    # _psi2_dS             NxQ
+    
+    mu2 = np.square(mu)
+    gamma2 = np.square(gamma)
+    variance2 = np.square(variance)
+    mu2S = mu2+S # NxQ
+    common_sum = np.einsum('nq,q,mq,nq->nm',gamma,variance,Z,mu) # NxM
+
+    dL_dvar = np.einsum('mo,nq,q,mq,oq->q',dL_dpsi2,2.*(gamma*mu2S-gamma2*mu2),variance,Z,Z)+\
+        np.einsum('mo,nq,mq,nq,no->q',dL_dpsi2,gamma,Z,mu,common_sum)+\
+        np.einsum('mo,nq,oq,nq,nm->q',dL_dpsi2,gamma,Z,mu,common_sum)
+        
+    dL_dgamma = np.einsum('mo,q,mq,oq,nq->nq',dL_dpsi2,variance2,Z,Z,(mu2S-2.*gamma*mu2))+\
+        np.einsum('mo,q,mq,nq,no->nq',dL_dpsi2,variance,Z,mu,common_sum)+\
+        np.einsum('mo,q,oq,nq,nm->nq',dL_dpsi2,variance,Z,mu,common_sum)
+    
+    dL_dmu = np.einsum('mo,q,mq,oq,nq,nq->nq',dL_dpsi2,variance2,Z,Z,mu,2.*(gamma-gamma2))+\
+        np.einsum('mo,nq,q,mq,no->nq',dL_dpsi2,gamma,variance,Z,common_sum)+\
+        np.einsum('mo,nq,q,oq,nm->nq',dL_dpsi2,gamma,variance,Z,common_sum)
+                    
+    dL_dS = np.einsum('mo,nq,q,mq,oq->nq',dL_dpsi2,gamma,variance2,Z,Z)
+    
+    dL_dZ = 2.*(np.einsum('om,nq,q,mq,nq->oq',dL_dpsi2,gamma,variance2,Z,mu2S)+np.einsum('om,nq,q,nq,nm->oq',dL_dpsi2,gamma,variance,mu,common_sum)
+                -np.einsum('om,nq,q,mq,nq->oq',dL_dpsi2,gamma2,variance2,Z,mu2))
+
+    return dL_dvar, dL_dgamma, dL_dmu, dL_dS, dL_dZ