You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
75 lines
2.5 KiB
75 lines
2.5 KiB
from typing import Optional, Union
|
|
|
|
from torch import Tensor
|
|
from torch.distributions import constraints
|
|
from torch.distributions.exponential import Exponential
|
|
from torch.distributions.transformed_distribution import TransformedDistribution
|
|
from torch.distributions.transforms import AffineTransform, ExpTransform
|
|
from torch.distributions.utils import broadcast_all
|
|
from torch.types import _size
|
|
|
|
|
|
__all__ = ["Pareto"]
|
|
|
|
|
|
class Pareto(TransformedDistribution):
|
|
r"""
|
|
Samples from a Pareto Type 1 distribution.
|
|
|
|
Example::
|
|
|
|
>>> # xdoctest: +IGNORE_WANT("non-deterministic")
|
|
>>> m = Pareto(torch.tensor([1.0]), torch.tensor([1.0]))
|
|
>>> m.sample() # sample from a Pareto distribution with scale=1 and alpha=1
|
|
tensor([ 1.5623])
|
|
|
|
Args:
|
|
scale (float or Tensor): Scale parameter of the distribution
|
|
alpha (float or Tensor): Shape parameter of the distribution
|
|
"""
|
|
|
|
arg_constraints = {"alpha": constraints.positive, "scale": constraints.positive}
|
|
|
|
def __init__(
|
|
self,
|
|
scale: Union[Tensor, float],
|
|
alpha: Union[Tensor, float],
|
|
validate_args: Optional[bool] = None,
|
|
) -> None:
|
|
self.scale, self.alpha = broadcast_all(scale, alpha)
|
|
base_dist = Exponential(self.alpha, validate_args=validate_args)
|
|
transforms = [ExpTransform(), AffineTransform(loc=0, scale=self.scale)]
|
|
# pyrefly: ignore [bad-argument-type]
|
|
super().__init__(base_dist, transforms, validate_args=validate_args)
|
|
|
|
def expand(
|
|
self, batch_shape: _size, _instance: Optional["Pareto"] = None
|
|
) -> "Pareto":
|
|
new = self._get_checked_instance(Pareto, _instance)
|
|
new.scale = self.scale.expand(batch_shape)
|
|
new.alpha = self.alpha.expand(batch_shape)
|
|
return super().expand(batch_shape, _instance=new)
|
|
|
|
@property
|
|
def mean(self) -> Tensor:
|
|
# mean is inf for alpha <= 1
|
|
a = self.alpha.clamp(min=1)
|
|
return a * self.scale / (a - 1)
|
|
|
|
@property
|
|
def mode(self) -> Tensor:
|
|
return self.scale
|
|
|
|
@property
|
|
def variance(self) -> Tensor:
|
|
# var is inf for alpha <= 2
|
|
a = self.alpha.clamp(min=2)
|
|
return self.scale.pow(2) * a / ((a - 1).pow(2) * (a - 2))
|
|
|
|
@constraints.dependent_property(is_discrete=False, event_dim=0)
|
|
def support(self) -> constraints.Constraint:
|
|
return constraints.greater_than_eq(self.scale)
|
|
|
|
def entropy(self) -> Tensor:
|
|
return (self.scale / self.alpha).log() + (1 + self.alpha.reciprocal())
|