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from numbers import Number
import torch
from torch.distributions import constraints
from torch.distributions.exp_family import ExponentialFamily
from torch.distributions.utils import broadcast_all
class Poisson(ExponentialFamily):
r"""
Creates a Poisson distribution parameterized by :attr:`rate`, the rate parameter.
Samples are nonnegative integers, with a pmf given by
.. math::
\mathrm{rate}^k \frac{e^{-\mathrm{rate}}}{k!}
Example::
>>> m = Poisson(torch.tensor([4]))
>>> m.sample()
tensor([ 3.])
Args:
rate (Number, Tensor): the rate parameter
"""
arg_constraints = {'rate': constraints.positive}
support = constraints.nonnegative_integer
@property
def mean(self):
return self.rate
@property
def variance(self):
return self.rate
def __init__(self, rate, validate_args=None):
self.rate, = broadcast_all(rate)
if isinstance(rate, Number):
batch_shape = torch.Size()
else:
batch_shape = self.rate.size()
super(Poisson, self).__init__(batch_shape, validate_args=validate_args)
def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(Poisson, _instance)
batch_shape = torch.Size(batch_shape)
new.rate = self.rate.expand(batch_shape)
super(Poisson, new).__init__(batch_shape, validate_args=False)
new._validate_args = self._validate_args
return new
def sample(self, sample_shape=torch.Size()):
shape = self._extended_shape(sample_shape)
with torch.no_grad():
return torch.poisson(self.rate.expand(shape))
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
rate, value = broadcast_all(self.rate, value)
return (rate.log() * value) - rate - (value + 1).lgamma()
@property
def _natural_params(self):
return (torch.log(self.rate), )
def _log_normalizer(self, x):
return torch.exp(x)
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