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
[docs]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 failure 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
logits (Tensor): Event log-odds for probabilities of success
"""
arg_constraints = {
'total_count': constraints.greater_than_eq(0),
'logits': constraints.real
}
support = constraints.nonnegative_integer
def __init__(self, total_count, logits, validate_args=None):
#logit = log(p/(1-p))
#p = e^l / (e^l + 1) = 1/(1 + e^(-l))
#-logits = logit(1-p)
self.total_count, self.logits, = broadcast_all(total_count, logits)
self.total_count = self.total_count.type_as(self.logits)
self._param = self.logits
batch_shape = self._param.size()
super(NegativeBinomial, self).__init__(batch_shape,
validate_args=validate_args)
[docs] 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):
"""mu = pr/(1-p)"""
return self.total_count * torch.exp(self.logits)
@property
def variance(self):
"""var = mu/(1-p) = mu*(1 + mu/r)"""
return self.mean / torch.sigmoid(-self.logits)
@property
def param_shape(self):
return self._param.size()
@lazy_property
def _gamma(self):
"""rate = (1-p)/p"""
# Note we avoid validating because self.total_count can be zero.
return torch.distributions.Gamma(concentration=self.total_count,
rate=torch.exp(-self.logits),
validate_args=False)
[docs] def sample(self, sample_shape=torch.Size()):
"""sample lambda = gamma(conc = r, rate = (1-p)/p)
sample y = Poisson(lambda)"""
with torch.no_grad():
rate = self._gamma.sample(sample_shape=sample_shape)
return torch.poisson(rate)
[docs] def log_prob(self, value):
"""binom(y+r-1, y) (1-p)^r p^y"""
# r*log(1-p) + y*log(p)
log_unnormalized_prob = (self.total_count * F.logsigmoid(-self.logits) +
value * F.logsigmoid(self.logits))
#-(gamma(y+r) - gamma(y+1) - gamma(r)) = log(binom(y+r-1, y)^(-1))
log_normalization = (-torch.lgamma(self.total_count + value) +
torch.lgamma(1. + value) +
torch.lgamma(self.total_count))
# binom(y+r-1, y) (1-p)^r p^y"""
return log_unnormalized_prob - log_normalization