| | 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 |
| |
|
| | __all__ = ['Gamma'] |
| |
|
| | 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:: |
| | |
| | >>> # xdoctest: +IGNORE_WANT("non-deterinistic") |
| | >>> 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) |
| | 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()) |
| |
|
