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linear kernel speed up

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This commit is contained in:
Zhenwen Dai 2014-11-20 17:38:19 +00:00
parent 11f872db33
commit 6ed91ce102
1 changed files with 20 additions and 14 deletions
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34
GPy/kern/_src/psi_comp/linear_psi_comp.py
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@ -6,6 +6,7 @@ The package for the Psi statistics computation of the linear kernel for Bayesian
""" """
import numpy as np import numpy as np
from ....util.linalg import tdot
def psicomputations(variance, Z, variational_posterior): def psicomputations(variance, Z, variational_posterior):
""" """
@ -19,9 +20,9 @@ def psicomputations(variance, Z, variational_posterior):
mu = variational_posterior.mean mu = variational_posterior.mean
S = variational_posterior.variance S = variational_posterior.variance
psi0 = np.einsum('q,nq->n',variance,np.square(mu)+S) psi0 = (variance*(np.square(mu)+S)).sum(axis=1)
psi1 = np.einsum('q,mq,nq->nm',variance,Z,mu) psi1 = np.dot(mu,(variance*Z).T)
psi2 = np.einsum('q,mq,oq,nq->mo',np.square(variance),Z,Z,S) + np.einsum('nm,no->mo',psi1,psi1) psi2 = np.dot(S.sum(axis=0)*np.square(variance)*Z,Z.T)+ tdot(psi1.T)
return psi0, psi1, psi2 return psi0, psi1, psi2
@ -33,10 +34,12 @@ def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, Z, variati
# Compute for psi0 and psi1 # Compute for psi0 and psi1
mu2S = np.square(mu)+S mu2S = np.square(mu)+S
dL_dvar += np.einsum('n,nq->q',dL_dpsi0,mu2S) + np.einsum('nm,mq,nq->q',dL_dpsi1,Z,mu) dL_dpsi0_var = dL_dpsi0[:,None]*variance[None,:]
dL_dmu += np.einsum('n,q,nq->nq',dL_dpsi0,2.*variance,mu) + np.einsum('nm,q,mq->nq',dL_dpsi1,variance,Z) dL_dpsi1_mu = np.dot(dL_dpsi1.T,mu)
dL_dS += np.einsum('n,q->nq',dL_dpsi0,variance) dL_dvar += (dL_dpsi0[:,None]*mu2S).sum(axis=0)+ (dL_dpsi1_mu*Z).sum(axis=0)
dL_dZ += np.einsum('nm,q,nq->mq',dL_dpsi1, variance,mu) dL_dmu += 2.*dL_dpsi0_var*mu+np.dot(dL_dpsi1,Z)*variance
dL_dS += dL_dpsi0_var
dL_dZ += dL_dpsi1_mu*variance
return dL_dvar, dL_dZ, dL_dmu, dL_dS return dL_dvar, dL_dZ, dL_dmu, dL_dS
@ -55,17 +58,20 @@ def _psi2computations(dL_dpsi2, variance, Z, mu, S):
# _psi2_dS NxQ # _psi2_dS NxQ
variance2 = np.square(variance) variance2 = np.square(variance)
common_sum = np.einsum('q,mq,nq->nm',variance,Z,mu) # NxM common_sum = np.dot(mu,(variance*Z).T)
Z_expect = np.einsum('mo,mq,oq->q',dL_dpsi2,Z,Z) Z_expect = (np.dot(dL_dpsi2,Z)*Z).sum(axis=0)
common_expect = np.einsum('mo,mq,no->nq',dL_dpsi2+dL_dpsi2.T,Z,common_sum) dL_dpsi2T = dL_dpsi2+dL_dpsi2.T
common_expect = np.dot(common_sum,np.dot(dL_dpsi2T,Z))
Z2_expect = np.inner(common_sum,dL_dpsi2T)
Z1_expect = np.dot(dL_dpsi2T,Z)
dL_dvar = np.einsum('q,nq,q->q',Z_expect,2.*S,variance)+ np.einsum('nq,nq->q',common_expect,mu) dL_dvar = 2.*S.sum(axis=0)*variance*Z_expect+(common_expect*mu).sum(axis=0)
dL_dmu = np.einsum('nq,q->nq',common_expect,variance) dL_dmu = common_expect*variance
dL_dS = np.empty(S.shape) dL_dS = np.empty(S.shape)
dL_dS[:] = np.einsum('q,q->q',Z_expect,variance2) dL_dS[:] = Z_expect*variance2
dL_dZ = 2.*(np.einsum('om,q,mq,nq->oq',dL_dpsi2,variance2,Z,S)+np.einsum('om,q,nq,nm->oq',dL_dpsi2,variance,mu,common_sum)) dL_dZ = variance2*S.sum(axis=0)*Z1_expect+np.dot(Z2_expect.T,variance*mu)
return dL_dvar, dL_dmu, dL_dS, dL_dZ return dL_dvar, dL_dmu, dL_dS, dL_dZ