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import torch
import torch.nn.functional as F
from torch.distributions import constraints
from torch.distributions.distribution import Distribution
from torch.distributions.utils import broadcast_all, probs_to_logits, lazy_property, logits_to_probs
class NegativeBinomial(Distribution):
r"""
Creates a Negative Binomial distribution, i.e. distribution
of the number of successful independent and identical Bernoulli trials
before :attr:`total_count` failures are achieved. The probability
of success of each Bernoulli trial is :attr:`probs`.
Args:
total_count (float or Tensor): non-negative number of negative Bernoulli
trials to stop, although the distribution is still valid for real
valued count
probs (Tensor): Event probabilities of success in the half open interval [0, 1)
logits (Tensor): Event log-odds for probabilities of success
"""
arg_constraints = {'total_count': constraints.greater_than_eq(0),
'probs': constraints.half_open_interval(0., 1.),
'logits': constraints.real}
support = constraints.nonnegative_integer
def __init__(self, total_count, probs=None, logits=None, validate_args=None):
if (probs is None) == (logits is None):
raise ValueError("Either `probs` or `logits` must be specified, but not both.")
if probs is not None:
self.total_count, self.probs, = broadcast_all(total_count, probs)
self.total_count = self.total_count.type_as(self.probs)
else:
self.total_count, self.logits, = broadcast_all(total_count, logits)
self.total_count = self.total_count.type_as(self.logits)
self._param = self.probs if probs is not None else self.logits
batch_shape = self._param.size()
super(NegativeBinomial, self).__init__(batch_shape, validate_args=validate_args)
def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(NegativeBinomial, _instance)
batch_shape = torch.Size(batch_shape)
new.total_count = self.total_count.expand(batch_shape)
if 'probs' in self.__dict__:
new.probs = self.probs.expand(batch_shape)
new._param = new.probs
if 'logits' in self.__dict__:
new.logits = self.logits.expand(batch_shape)
new._param = new.logits
super(NegativeBinomial, new).__init__(batch_shape, validate_args=False)
new._validate_args = self._validate_args
return new
def _new(self, *args, **kwargs):
return self._param.new(*args, **kwargs)
@property
def mean(self):
return self.total_count * torch.exp(self.logits)
@property
def variance(self):
return self.mean / torch.sigmoid(-self.logits)
@lazy_property
def logits(self):
return probs_to_logits(self.probs, is_binary=True)
@lazy_property
def probs(self):
return logits_to_probs(self.logits, is_binary=True)
@property
def param_shape(self):
return self._param.size()
@lazy_property
def _gamma(self):
return torch.distributions.Gamma(concentration=self.total_count,
rate=torch.exp(-self.logits))
def sample(self, sample_shape=torch.Size()):
with torch.no_grad():
rate = self._gamma.sample(sample_shape=sample_shape)
return torch.poisson(rate)
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
log_unnormalized_prob = (self.total_count * F.logsigmoid(-self.logits) +
value * F.logsigmoid(self.logits))
log_normalization = (-torch.lgamma(self.total_count + value) + torch.lgamma(1. + value) +
torch.lgamma(self.total_count))
return log_unnormalized_prob - log_normalization
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