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[missing data] general implementation for subsetting data

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This commit is contained in:
Max Zwiessele 2014-10-08 12:03:51 +01:00
parent d93fac8c13
commit fa7807ee6f
7 changed files with 329 additions and 108 deletions
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29
GPy/kern/_src/psi_comp/rbf_psi_comp.py
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@ -17,7 +17,7 @@ def psicomputations(variance, lengthscale, Z, variational_posterior):
# _psi1 NxM
mu = variational_posterior.mean
S = variational_posterior.variance
psi0 = np.empty(mu.shape[0])
psi0[:] = variance
psi1 = _psi1computations(variance, lengthscale, Z, mu, S)
@ -41,7 +41,7 @@ def __psi1computations(variance, lengthscale, Z, mu, S):
_psi1_logdenom = np.log(S/lengthscale2+1.).sum(axis=-1) # N
_psi1_log = (_psi1_logdenom[:,None]+np.einsum('nmq,nq->nm',np.square(mu[:,None,:]-Z[None,:,:]),1./(S+lengthscale2)))/(-2.)
_psi1 = variance*np.exp(_psi1_log)
return _psi1
def __psi2computations(variance, lengthscale, Z, mu, S):
@ -54,27 +54,27 @@ def __psi2computations(variance, lengthscale, Z, mu, S):
# here are the "statistics" for psi2
# Produced intermediate results:
# _psi2 MxM
lengthscale2 = np.square(lengthscale)
_psi2_logdenom = np.log(2.*S/lengthscale2+1.).sum(axis=-1)/(-2.) # N
_psi2_exp1 = (np.square(Z[:,None,:]-Z[None,:,:])/lengthscale2).sum(axis=-1)/(-4.) #MxM
Z_hat = (Z[:,None,:]+Z[None,:,:])/2. #MxMxQ
denom = 1./(2.*S+lengthscale2)
_psi2_exp2 = -(np.square(mu)*denom).sum(axis=-1)[:,None,None]+2.*np.einsum('nq,moq,nq->nmo',mu,Z_hat,denom)-np.einsum('moq,nq->nmo',np.square(Z_hat),denom)
_psi2 = variance*variance*np.exp(_psi2_logdenom[:,None,None]+_psi2_exp1[None,:,:]+_psi2_exp2)
return _psi2
def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):
ARD = (len(lengthscale)!=1)
dvar_psi1, dl_psi1, dZ_psi1, dmu_psi1, dS_psi1 = _psi1compDer(dL_dpsi1, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance)
dvar_psi2, dl_psi2, dZ_psi2, dmu_psi2, dS_psi2 = _psi2compDer(dL_dpsi2, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance)
dL_dvar = np.sum(dL_dpsi0) + dvar_psi1 + dvar_psi2
dL_dlengscale = dl_psi1 + dl_psi2
if not ARD:
dL_dlengscale = dL_dlengscale.sum()
@ -82,7 +82,7 @@ def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscal
dL_dmu = dmu_psi1 + dmu_psi2
dL_dS = dS_psi1 + dS_psi2
dL_dZ = dZ_psi1 + dZ_psi2
return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS
def _psi1compDer(dL_dpsi1, variance, lengthscale, Z, mu, S):
@ -101,9 +101,9 @@ def _psi1compDer(dL_dpsi1, variance, lengthscale, Z, mu, S):
# _dL_dgamma NxQ
# _dL_dmu NxQ
# _dL_dS NxQ
lengthscale2 = np.square(lengthscale)
_psi1 = _psi1computations(variance, lengthscale, Z, mu, S)
Lpsi1 = dL_dpsi1*_psi1
Zmu = Z[None,:,:]-mu[:,None,:] # NxMxQ
@ -114,7 +114,7 @@ def _psi1compDer(dL_dpsi1, variance, lengthscale, Z, mu, S):
_dL_dS = np.einsum('nm,nmq,nq->nq',Lpsi1,(Zmu2_denom-1.),denom)/2.
_dL_dZ = -np.einsum('nm,nmq,nq->mq',Lpsi1,Zmu,denom)
_dL_dl = np.einsum('nm,nmq,nq->q',Lpsi1,(Zmu2_denom+(S/lengthscale2)[:,None,:]),denom*lengthscale)
return _dL_dvar, _dL_dl, _dL_dZ, _dL_dmu, _dL_dS
def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S):
@ -133,13 +133,12 @@ def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S):
# _dL_dgamma NxQ
# _dL_dmu NxQ
# _dL_dS NxQ
lengthscale2 = np.square(lengthscale)
denom = 1./(2*S+lengthscale2)
denom2 = np.square(denom)
_psi2 = _psi2computations(variance, lengthscale, Z, mu, S) # NxMxM
Lpsi2 = dL_dpsi2[None,:,:]*_psi2
Lpsi2sum = np.einsum('nmo->n',Lpsi2) #N
Lpsi2Z = np.einsum('nmo,oq->nq',Lpsi2,Z) #NxQ
@ -147,7 +146,7 @@ def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S):
Lpsi2Z2p = np.einsum('nmo,mq,oq->nq',Lpsi2,Z,Z) #NxQ
Lpsi2Zhat = Lpsi2Z
Lpsi2Zhat2 = (Lpsi2Z2+Lpsi2Z2p)/2
_dL_dvar = Lpsi2sum.sum()*2/variance
_dL_dmu = (-2*denom) * (mu*Lpsi2sum[:,None]-Lpsi2Zhat)
_dL_dS = (2*np.square(denom))*(np.square(mu)*Lpsi2sum[:,None]-2*mu*Lpsi2Zhat+Lpsi2Zhat2) - denom*Lpsi2sum[:,None]
@ -157,6 +156,6 @@ def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S):
(2*mu*denom2)*Lpsi2Zhat+denom2*Lpsi2Zhat2).sum(axis=0)
return _dL_dvar, _dL_dl, _dL_dZ, _dL_dmu, _dL_dS
_psi1computations = Cacher(__psi1computations, limit=1)
_psi2computations = Cacher(__psi2computations, limit=1)