def log_prob(self, value):
"""Log of probability densitiy function.
Args:
value (Tensor): Value to be evaluated.
"""
return ((paddle.log(value) * (self.concentration - 1.0)).sum(-1) +
paddle.lgamma(self.concentration.sum(-1)) -
paddle.lgamma(self.concentration).sum(-1))
def _binomial_logpmf(self, count, value):
logits = self._probs_to_logits(self.probs, is_binary=True)
factor_n = paddle.lgamma(count + 1)
factor_k = paddle.lgamma(value + 1)
factor_nmk = paddle.lgamma(count - value + 1)
norm = (count * _clip_by_zero(logits) +
count * paddle.log1p(paddle.exp(-paddle.abs(logits))) -
factor_n)
return value * logits - factor_k - factor_nmk - norm
def entropy(self):
"""Entropy of Dirichlet distribution.
Returns:
Entropy of distribution.
"""
concentration0 = self.concentration.sum(-1)
k = self.concentration.shape[-1]
return (paddle.lgamma(self.concentration).sum(-1) -
paddle.lgamma(concentration0) -
(k - concentration0) * paddle.digamma(concentration0) -
((self.concentration - 1.0) *
paddle.digamma(self.concentration)).sum(-1))
def entropy(self):
"""entropy of multinomial distribution
Returns:
Tensor: entropy value
"""
n = paddle.full(shape=[1],
fill_value=self.total_count,
dtype=self.probs.dtype)
support = paddle.arange(
self.total_count + 1,
dtype=self.probs.dtype).reshape((-1, ) +
(1, ) * len(self.probs.shape))[1:]
binomial_pmf = paddle.exp(self._binomial_logpmf(n, support))
return ((n * self._categorical.entropy() - paddle.lgamma(n + 1)) +
((binomial_pmf * paddle.lgamma(support + 1)).sum([0, -1])))
def log_prob(self, value):
"""probability mass function evaluated at value
Args:
value (Tensor): value to be evaluated.
Returns:
Tensor: probability of value.
"""
if paddle.is_integer(value):
value = paddle.cast(value, self.probs.dtype)
logits, value = paddle.broadcast_tensors(
[paddle.log(self.probs), value])
logits[(value == 0) & (paddle.isinf(logits))] = 0
return (paddle.lgamma(value.sum(-1) + 1) -
paddle.lgamma(value + 1).sum(-1) + (value * logits).sum(-1))
def _log_normalizer(self, x, y):
return paddle.lgamma(x) + paddle.lgamma(y) - paddle.lgamma(x + y)
def _log_normalizer(self, x):
return x.lgamma().sum(-1) - paddle.lgamma(x.sum(-1))
