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performance improvement for sslinear kernel

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This commit is contained in:
Zhenwen Dai 2014-11-20 14:52:49 +00:00
parent aa473178f7
commit 11f872db33
1 changed files with 16 additions and 7 deletions
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23
GPy/kern/_src/psi_comp/sslinear_psi_comp.py
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@ -5,6 +5,8 @@
The package for the Psi statistics computation of the linear kernel for SSGPLVM
"""
from ....util.linalg import tdot
import numpy as np
def psicomputations(variance, Z, variational_posterior):
@ -20,10 +22,9 @@ def psicomputations(variance, Z, variational_posterior):
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)
psi2 = np.einsum('nq,q,mq,oq,nq->mo',gamma,np.square(variance),Z,Z,(1-gamma)*np.square(mu)+S) +\
np.einsum('nm,no->mo',psi1,psi1)
psi0 = (gamma*(np.square(mu)+S)*variance).sum(axis=-1)
psi1 = np.inner(variance*gamma*mu,Z)
psi2 = np.inner(np.square(variance)*(gamma*((1-gamma)*np.square(mu)+S)).sum(axis=0)*Z,Z)+tdot(psi1.T)
return psi0, psi1, psi2
@ -63,9 +64,16 @@ def _psi2computations(dL_dpsi2, variance, Z, mu, S, gamma):
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
gvm = np.einsum('nq,nq,q->nq',gamma,mu,variance)
common_sum = np.einsum('nq,mq->nm',gvm,Z)
# common_sum = np.einsum('nq,q,mq,nq->nm',gamma,variance,Z,mu) # NxM
Z_expect = np.einsum('mo,mq,oq->q',dL_dpsi2,Z,Z)
common_expect = np.einsum('mo,mq,no->nq',dL_dpsi2+dL_dpsi2.T,Z,common_sum)
dL_dpsi2T = dL_dpsi2+dL_dpsi2.T
tmp = np.einsum('mo,oq->mq',dL_dpsi2T,Z)
common_expect = np.einsum('mq,nm->nq',tmp,common_sum)
# common_expect = np.einsum('mo,mq,no->nq',dL_dpsi2+dL_dpsi2.T,Z,common_sum)
Z2_expect = np.einsum('om,nm->no',dL_dpsi2T,common_sum)
Z1_expect = np.einsum('om,mq->oq',dL_dpsi2T,Z)
dL_dvar = np.einsum('nq,q,q->q',2.*(gamma*mu2S-gamma2*mu2),variance,Z_expect)+\
np.einsum('nq,nq,nq->q',common_expect,gamma,mu)
@ -78,6 +86,7 @@ def _psi2computations(dL_dpsi2, variance, Z, mu, S, gamma):
dL_dS = np.einsum('q,nq,q->nq',Z_expect,gamma,variance2)
dL_dZ = 2.*(np.einsum('om,nq,q,mq,nq->oq',dL_dpsi2,gamma,variance2,Z,(mu2S-gamma*mu2))+np.einsum('om,nq,q,nq,nm->oq',dL_dpsi2,gamma,variance,mu,common_sum))
# dL_dZ = 2.*(np.einsum('om,nq,q,mq,nq->oq',dL_dpsi2,gamma,variance2,Z,(mu2S-gamma*mu2))+np.einsum('om,nq,q,nq,nm->oq',dL_dpsi2,gamma,variance,mu,common_sum))
dL_dZ = Z1_expect*np.einsum('nq,q,nq->q',gamma,variance2,(mu2S-gamma*mu2))+np.einsum('nq,q,nq,nm->mq',gamma,variance,mu,Z2_expect)
return dL_dvar, dL_dgamma, dL_dmu, dL_dS, dL_dZ