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import torch
from torch.distributions import constraints
from torch.distributions.gamma import Gamma
from torch.distributions.transformed_distribution import TransformedDistribution
from torch.distributions.transforms import PowerTransform
__all__ = ["InverseGamma"]
class InverseGamma(TransformedDistribution):
r"""
Creates an inverse gamma distribution parameterized by :attr:`concentration` and :attr:`rate`
where::
X ~ Gamma(concentration, rate)
Y = 1 / X ~ InverseGamma(concentration, rate)
Example::
>>> # xdoctest: +IGNORE_WANT("non-deterinistic")
>>> m = InverseGamma(torch.tensor([2.0]), torch.tensor([3.0]))
>>> m.sample()
tensor([ 1.2953])
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.positive
has_rsample = True
def __init__(self, concentration, rate, validate_args=None):
base_dist = Gamma(concentration, rate, validate_args=validate_args)
neg_one = -base_dist.rate.new_ones(())
super().__init__(
base_dist, PowerTransform(neg_one), validate_args=validate_args
)
def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(InverseGamma, _instance)
return super().expand(batch_shape, _instance=new)
@property
def concentration(self):
return self.base_dist.concentration
@property
def rate(self):
return self.base_dist.rate
@property
def mean(self):
result = self.rate / (self.concentration - 1)
return torch.where(self.concentration > 1, result, torch.inf)
@property
def mode(self):
return self.rate / (self.concentration + 1)
@property
def variance(self):
result = self.rate.square() / (
(self.concentration - 1).square() * (self.concentration - 2)
)
return torch.where(self.concentration > 2, result, torch.inf)
def entropy(self):
return (
self.concentration
+ self.rate.log()
+ self.concentration.lgamma()
- (1 + self.concentration) * self.concentration.digamma()
)
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