| 1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980818283848586 |
- 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.nonnegative
- has_rsample = True
- _mean_carrier_measure = 0
- @property
- def mean(self):
- return self.concentration / self.rate
- @property
- def mode(self):
- return ((self.concentration - 1) / self.rate).clamp(min=0)
- @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 (torch.xlogy(self.concentration, self.rate) +
- torch.xlogy(self.concentration - 1, 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())
|
