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