def log_likelihood_lower_bound(self, x):
x_sequence = tensor.tile(x.dimshuffle('x', 0, 1), (self.T, 1, 1))
rval = self.apply(x_sequence)
c_states, mu_phi, log_sigma_phi = rval[0], rval[-2], rval[-1]
prior_mu = self.prior_mu.dimshuffle('x', 'x', 0)
prior_log_sigma = self.prior_log_sigma.dimshuffle('x', 'x', 0)
kl_term = (
prior_log_sigma - log_sigma_phi +
0.5 * (
tensor.exp(2 * log_sigma_phi) + (mu_phi - prior_mu) ** 2
) / tensor.exp(2 * prior_log_sigma) - 0.5).sum(axis=2).sum(axis=0)
kl_term.name = 'kl_term'
reconstruction_term = - (
x * tensor.nnet.softplus(-c_states[-1]) +
(1 - x) * tensor.nnet.softplus(c_states[-1])).sum(axis=1)
reconstruction_term.name = 'reconstruction_term'
log_likelihood_lower_bound = reconstruction_term - kl_term
log_likelihood_lower_bound.name = 'log_likelihood_lower_bound'
annotation = Annotation()
annotation.add_auxiliary_variable(kl_term, name='kl_term')
annotation.add_auxiliary_variable(-reconstruction_term,
name='reconstruction_term')
add_annotation(log_likelihood_lower_bound, annotation)
return log_likelihood_lower_bound
def annotate_update(self, update, tag_to):
a = Annotation()
for (var, up) in update:
a.updates[var] = up
add_annotation(tag_to, a)
def annotate_update(self, update, tag_to):
a = Annotation()
for (var, up) in update:
a.updates[var] = up
add_annotation(tag_to, a)