def elbo(self, variational_posterior, datas, inputs=None, masks=None, tags=None, n_samples=1):
"""
Lower bound on the marginal likelihood p(y | theta)
using variational posterior q(x; phi) where phi = variational_params
"""
elbo = 0
for sample in range(n_samples):
# Sample x from the variational posterior
xs = variational_posterior.sample()
# log p(theta)
elbo += self.log_prior()
# log p(x, y | theta) = log \sum_z p(x, y, z | theta)
for x, data, input, mask, tag in zip(xs, datas, inputs, masks, tags):
# The "mask" for x is all ones
x_mask = np.ones_like(x, dtype=bool)
pi0 = self.init_state_distn.initial_state_distn
Ps = self.transitions.transition_matrices(x, input, x_mask, tag)
log_likes = self.dynamics.log_likelihoods(x, input, x_mask, tag)
log_likes += self.emissions.log_likelihoods(data, input, mask, tag, x)
elbo += hmm_normalizer(pi0, Ps, log_likes)
# -log q(x)
elbo -= variational_posterior.log_density(xs)
assert np.isfinite(elbo)
return elbo / n_samples
def elbo(self, variational_params, datas, inputs=None, masks=None, tags=None, n_samples=1):
"""
Lower bound on the marginal likelihood p(y | theta)
using variational posterior q(x; phi) where phi = variational_params
"""
elbo = 0
for data, input, mask, tag, (q_mu, q_sigma_inv) in \
zip(datas, inputs, masks, tags, variational_params):
q_sigma = np.exp(q_sigma_inv)
for sample in range(n_samples):
# log p(theta)
elbo += self.log_prior()
# Sample x from the variational posterior
x = q_mu + np.sqrt(q_sigma) * npr.randn(data.shape[0], self.D)
# Compute log p(x | theta) = log \sum_z p(x, z | theta)
# The "mask" for x is all ones
x_mask = np.ones_like(x, dtype=bool)
log_pi0 = self.init_state_distn.log_initial_state_distn(x, input, x_mask, tag)
log_Ps = self.transitions.log_transition_matrices(x, input, x_mask, tag)
log_likes = self.dynamics.log_likelihoods(x, input, x_mask, tag)
log_likes += self.emissions.log_likelihoods(data, input, mask, tag, x)
elbo += hmm_normalizer(log_pi0, log_Ps, log_likes)
# -log q(x)
elbo -= np.sum(-0.5 * np.log(2 * np.pi * q_sigma))
elbo -= np.sum(-0.5 * (x - q_mu)**2 / q_sigma)
assert np.isfinite(elbo)
return elbo / n_samples
def log_likelihood(self, datas, inputs=None, masks=None, tags=None):
"""
Compute the log probability of the data under the current
model parameters.
:param datas: single array or list of arrays of data.
:return total log probability of the data.
"""
ll = 0
for data, input, mask, tag in zip(datas, inputs, masks, tags):
log_pi0 = self.init_state_distn.log_initial_state_distn(data, input, mask, tag)
log_Ps = self.transitions.log_transition_matrices(data, input, mask, tag)
log_likes = self.observations.log_likelihoods(data, input, mask, tag)
ll += hmm_normalizer(log_pi0, log_Ps, log_likes)
assert np.isfinite(ll)
return ll
