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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
def _standard_gamma(concentration):
return torch._standard_gamma(concentration)
class Gamma(ExponentialFamily):
r"""
Creates a Gamma distribution parameterized by shape :attr:`concentration` and :attr:`rate`.
Example::
>>> m = Gamma(torch.tensor([1.0]), torch.tensor([1.0]))
>>> m.sample() # Gamma distributed with concentration=1 and rate=1
tensor([ 0.1046])
Args:
concentration (float or Tensor): shape parameter of the distribution
(often referred to as alpha)
rate (float or Tensor): rate = 1 / scale of the distribution
(often referred to as beta)
"""
arg_constraints = {'concentration': constraints.positive, 'rate': constraints.positive}
support = constraints.positive
has_rsample = True
_mean_carrier_measure = 0
@property
def mean(self):
return self.concentration / self.rate
@property
def variance(self):
return self.concentration / self.rate.pow(2)
def __init__(self, concentration, rate, validate_args=None):
self.concentration, self.rate = broadcast_all(concentration, rate)
if isinstance(concentration, Number) and isinstance(rate, Number):
batch_shape = torch.Size()
else:
batch_shape = self.concentration.size()
super(Gamma, self).__init__(batch_shape, validate_args=validate_args)
def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(Gamma, _instance)
batch_shape = torch.Size(batch_shape)
new.concentration = self.concentration.expand(batch_shape)
new.rate = self.rate.expand(batch_shape)
super(Gamma, new).__init__(batch_shape, validate_args=False)
new._validate_args = self._validate_args
return new
def rsample(self, sample_shape=torch.Size()):
shape = self._extended_shape(sample_shape)
value = _standard_gamma(self.concentration.expand(shape)) / self.rate.expand(shape)
value.detach().clamp_(min=torch.finfo(value.dtype).tiny) # do not record in autograd graph
return value
def log_prob(self, value):
value = torch.as_tensor(value, dtype=self.rate.dtype, device=self.rate.device)
if self._validate_args:
self._validate_sample(value)
return (self.concentration * torch.log(self.rate) +
(self.concentration - 1) * torch.log(value) -
self.rate * value - torch.lgamma(self.concentration))
def entropy(self):
return (self.concentration - torch.log(self.rate) + torch.lgamma(self.concentration) +
(1.0 - self.concentration) * torch.digamma(self.concentration))
@property
def _natural_params(self):
return (self.concentration - 1, -self.rate)
def _log_normalizer(self, x, y):
return torch.lgamma(x + 1) + (x + 1) * torch.log(-y.reciprocal())
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