def gaussian_meanfield(gaussian_globals, node_potentials, label_stats):
# Ref. Eq 39
# gaussian_globals = E_{q(\mu, \Sigma)}[t(\mu, \Sigma)] here q(\mu, \Sigma) is posterior which is NIW. Shape = (K, 4, 4)
# label_stats = E_{q(z)}[t(z)] -> categorical expected statistics. Shape = (batch_size, K)
# stats = E_{q(z)}[t(z)] -> Gaussian expected statistics Shape = (batch_size, 4, 4)
# node_potentials = r(\phi, y) Shape = (batch_size, 4, 4)
#print gaussian_globals.shape, node_potentials.shape, label_stats.shape
global_potentials = np.tensordot(label_stats, gaussian_globals, [1, 0])
natparam = node_potentials + global_potentials #using Eq. 39
stats = gaussian.expectedstats(natparam)
#print stats.shape
kl = np.tensordot(node_potentials, stats, 3) - gaussian.logZ(natparam)
return natparam, stats, kl
def gaussian_meanfield(gaussian_globals, node_potentials, label_stats):
global_potentials = np.tensordot(label_stats, gaussian_globals, [1, 0])
natparam = node_potentials + global_potentials
stats = gaussian.expectedstats(natparam)
kl = np.tensordot(node_potentials, stats, 3) - gaussian.logZ(natparam)
return natparam, stats, kl
def gaussian_kl(gaussian_globals, label_stats, natparam, stats):
global_potentials = np.tensordot(label_stats, gaussian_globals, [1, 0])
return np.tensordot(natparam - global_potentials, stats, 3) - gaussian.logZ(natparam)