def log_partition_function(natural_params, data):
if isinstance(data, list):
return sum(map(partial(log_partition_function, natural_params), data))
log_pi, log_A, log_B = natural_params
log_alpha = log_pi
for y in data:
log_alpha = logsumexp(log_alpha[:,None] + log_A, axis=0) + log_B[:,y]
return logsumexp(log_alpha)
def log_marginal_likelihood(params, data):
cluster_lls = []
for log_proportion, mean, chol in zip(*unpack_params(params)):
cov = np.dot(chol.T, chol) + 0.000001 * np.eye(D)
cluster_log_likelihood = log_proportion + mvn.logpdf(data, mean, cov)
cluster_lls.append(np.expand_dims(cluster_log_likelihood, axis=0))
cluster_lls = np.concatenate(cluster_lls, axis=0)
return np.sum(logsumexp(cluster_lls, axis=0))
def unpack_params(params):
"""Unpacks parameter vector into the proportions, means and covariances
of each mixture component. The covariance matrices are parametrized by
their Cholesky decompositions."""
log_proportions = parser.get(params, 'log proportions')
normalized_log_proportions = log_proportions - logsumexp(log_proportions)
means = parser.get(params, 'means')
lower_tris = np.tril(parser.get(params, 'lower triangles'), k=-1)
diag_chols = np.exp( parser.get(params, 'log diagonals'))
chols = []
for lower_tri, diag in zip(lower_tris, diag_chols):
chols.append(np.expand_dims(lower_tri + np.diag(diag), 0))
chols = np.concatenate(chols, axis=0)
return normalized_log_proportions, means, chols
def predictions(W_vect, inputs):
for W, b in unpack_layers(W_vect):
outputs = np.dot(inputs, W) + b
inputs = np.tanh(outputs)
return outputs - logsumexp(outputs, axis=1, keepdims=True)
