| |
| from typing import Optional, Union |
|
|
| import torch |
| from torch import Tensor |
| from torch.distributions import constraints |
| from torch.distributions.exp_family import ExponentialFamily |
| from torch.distributions.utils import broadcast_all |
| from torch.types import _Number, _size |
|
|
|
|
| __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-deterministic") |
| >>> 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 parameter of the distribution |
| (often referred to as beta), rate = 1 / scale |
| """ |
|
|
| arg_constraints = { |
| "concentration": constraints.positive, |
| "rate": constraints.positive, |
| } |
| support = constraints.nonnegative |
| has_rsample = True |
| _mean_carrier_measure = 0 |
|
|
| @property |
| def mean(self) -> Tensor: |
| return self.concentration / self.rate |
|
|
| @property |
| def mode(self) -> Tensor: |
| return ((self.concentration - 1) / self.rate).clamp(min=0) |
|
|
| @property |
| def variance(self) -> Tensor: |
| return self.concentration / self.rate.pow(2) |
|
|
| def __init__( |
| self, |
| concentration: Union[Tensor, float], |
| rate: Union[Tensor, float], |
| validate_args: Optional[bool] = None, |
| ) -> 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().__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: _size = torch.Size()) -> Tensor: |
| 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) -> tuple[Tensor, Tensor]: |
| return (self.concentration - 1, -self.rate) |
|
|
| def _log_normalizer(self, x, y): |
| return torch.lgamma(x + 1) + (x + 1) * torch.log(-y.reciprocal()) |
|
|
| def cdf(self, value): |
| if self._validate_args: |
| self._validate_sample(value) |
| return torch.special.gammainc(self.concentration, self.rate * value) |
|
|
