|
|
|
|
|
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, 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().__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) |
|
|
|
