def label_meanfield(label_global, gaussian_globals, gaussian_stats):
node_potentials = np.tensordot(gaussian_stats, gaussian_globals,
[[1, 2], [1, 2]])
natparam = node_potentials + label_global
stats = categorical.expectedstats(natparam)
kl = np.tensordot(stats, node_potentials) - categorical.logZ(natparam)
return natparam, stats, kl
def label_meanfield(label_global, gaussian_globals, gaussian_stats):
# Ref. Eq 39
# label_global = E_{q(\pi)}[t(\pi)] where q(\pi) is dirichlet and t(\pi) is {log\pi_i}
# stats = E_{q(z)}[t(z)] -> categorical expected statistics
# gaussian_stats = E_{q(x)}[t(x)] where q(x) is NIW and t(x) is [x, xxT]
# gaussian_globals = \eta_x^0(\theta)
node_potentials = np.tensordot(gaussian_stats, gaussian_globals, [[1,2], [1,2]])
natparam = node_potentials + label_global
stats = categorical.expectedstats(natparam)
kl = np.tensordot(stats, node_potentials) - categorical.logZ(natparam)
return natparam, stats, kl
def label_meanfield(label_global, gaussian_globals, gaussian_suff_stats):
# Ref. Eq 39
# label_global = E_{q(\pi)}[t(\pi)] where q(\pi) is dirichlet and t(\pi) is {log\pi_i}
# stats = E_{q(z)}[t(z)] -> categorical expected statistics
# gaussian_suff_stats = t(x) where t(x) is [x, xxT] Shape = (batch_size, 4, 4)
# gaussian_globals = niw expected stats (Shape = (K, 4, 4))
# node_potenials, label_global, natparam Shape = (batch_size, K)
node_potentials = np.tensordot(gaussian_suff_stats, gaussian_globals,
[[1, 2], [1, 2]])
natparam = node_potentials + label_global
stats = categorical.expectedstats(natparam)
kl = np.tensordot(stats, node_potentials) - categorical.logZ(natparam)
return natparam, stats, kl
def label_meanfield(label_global, gaussian_globals, gaussian_stats):
node_potentials = np.tensordot(gaussian_stats, gaussian_globals, [[1,2], [1,2]])
natparam = node_potentials + label_global
stats = categorical.expectedstats(natparam)
kl = np.tensordot(stats, node_potentials) - categorical.logZ(natparam)
return natparam, stats, kl
def label_kl(label_global, natparam, stats):
return np.tensordot(stats, natparam - label_global) - categorical.logZ(natparam)