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Fixed quadrature for bernoulli likelihood, started adding Gaussian likelihood derivatives for quadrature

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This commit is contained in:
Alan Saul 2014-12-19 17:53:32 +00:00
parent 2de2217473
commit 935f2016db
5 changed files with 23 additions and 35 deletions
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24
GPy/inference/latent_function_inference/svgp.py
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@ -5,27 +5,9 @@ import numpy as np
from posterior import Posterior
class SVGP(LatentFunctionInference):
def likelihood_quadrature(self, Y, m, v):
Ysign = np.where(Y==1,1,-1).flatten()
from scipy import stats
self.gh_x, self.gh_w = np.polynomial.hermite.hermgauss(20)
#assume probit for now.
X = self.gh_x[None,:]*np.sqrt(2.*v[:,None]) + (m*Ysign)[:,None]
p = stats.norm.cdf(X)
p = np.clip(p, 1e-9, 1.-1e-9) # for numerical stability
N = stats.norm.pdf(X)
F = np.log(p).dot(self.gh_w)
NoverP = N/p
dF_dm = (NoverP*Ysign[:,None]).dot(self.gh_w)
dF_dv = -0.5*(NoverP**2 + NoverP*X).dot(self.gh_w)
return F, dF_dm, dF_dv
def inference(self, q_u_mean, q_u_chol, kern, X, Z, likelihood, Y, Y_metadata=None):
assert Y.shape[1]==1, "multi outputs not implemented"
num_inducing = Z.shape[0]
#expand cholesky representation
L = choleskies.flat_to_triang(q_u_chol[:,None]).squeeze()
@ -57,9 +39,7 @@ class SVGP(LatentFunctionInference):
dKL_dKmm = 0.5*Kmmi - 0.5*Kmmi.dot(S).dot(Kmmi) - 0.5*Kmmim[:,None]*Kmmim[None,:]
#quadrature for the likelihood
#F, dF_dmu, dF_dv = likelihood.variational_expectations(Y, mu, v)
F, dF_dmu, dF_dv = self.likelihood_quadrature(Y, mu, v)
F, dF_dmu, dF_dv, dF_dthetaL = likelihood.variational_expectations(Y, mu, v)
#rescale the F term if working on a batch
#F, dF_dmu, dF_dv = F*batch_scale, dF_dmu*batch_scale, dF_dv*batch_scale
@ -82,7 +62,7 @@ class SVGP(LatentFunctionInference):
dL_dchol = 2.*np.dot(dL_dS, L)
dL_dchol = choleskies.triang_to_flat(dL_dchol[:,:,None]).squeeze()
return Posterior(mean=q_u_mean, cov=S, K=Kmm), log_marginal, {'dL_dKmm':dL_dKmm, 'dL_dKmn':dL_dKmn, 'dL_dKdiag': dF_dv, 'dL_dm':dL_dm, 'dL_dchol':dL_dchol}
return Posterior(mean=q_u_mean, cov=S, K=Kmm), log_marginal, {'dL_dKmm':dL_dKmm, 'dL_dKmn':dL_dKmn, 'dL_dKdiag': dF_dv, 'dL_dm':dL_dm, 'dL_dchol':dL_dchol, 'dL_dthetaL':dF_dthetaL}