61 lines
2.1 KiB
Python
61 lines
2.1 KiB
Python
|
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
|
||
|
|
|
||
|
|
__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, alpha, validate_args=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)]
|
||
|
|
super().__init__(base_dist, transforms, validate_args=validate_args)
|
||
|
|
|
||
|
|
def expand(self, batch_shape, _instance=None):
|
||
|
|
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):
|
||
|
|
# mean is inf for alpha <= 1
|
||
|
|
a = self.alpha.clamp(min=1)
|
||
|
|
return a * self.scale / (a - 1)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def mode(self):
|
||
|
|
return self.scale
|
||
|
|
|
||
|
|
@property
|
||
|
|
def variance(self):
|
||
|
|
# 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):
|
||
|
|
return constraints.greater_than_eq(self.scale)
|
||
|
|
|
||
|
|
def entropy(self):
|
||
|
|
return (self.scale / self.alpha).log() + (1 + self.alpha.reciprocal())
|