# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0
import math
import torch
from torch.distributions import constraints
from torch.distributions.utils import broadcast_all
from .torch_distribution import TorchDistribution
[docs]class SoftLaplace(TorchDistribution):
"""
Smooth distribution with Laplace-like tail behavior.
This distribution corresponds to the log-convex density::
z = (value - loc) / scale
log_prob = log(2 / pi) - log(scale) - logaddexp(z, -z)
Like the Laplace density, this density has the heaviest possible tails
(asymptotically) while still being log-convex. Unlike the Laplace
distribution, this distribution is infinitely differentiable everywhere,
and is thus suitable for constructing Laplace approximations.
:param loc: Location parameter.
:param scale: Scale parameter.
"""
arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
support = constraints.real
has_rsample = True
def __init__(self, loc, scale, *, validate_args=None):
self.loc, self.scale = broadcast_all(loc, scale)
super().__init__(self.loc.shape, validate_args=validate_args)
[docs] def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(SoftLaplace, _instance)
batch_shape = torch.Size(batch_shape)
new.loc = self.loc.expand(batch_shape)
new.scale = self.scale.expand(batch_shape)
super(SoftLaplace, new).__init__(batch_shape, validate_args=False)
new._validate_args = self._validate_args
return new
[docs] def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
z = (value - self.loc) / self.scale
return math.log(2 / math.pi) - self.scale.log() - torch.logaddexp(z, -z)
[docs] def rsample(self, sample_shape=torch.Size()):
shape = self._extended_shape(sample_shape)
u = self.loc.new_empty(shape).uniform_()
return self.icdf(u)
[docs] def cdf(self, value):
if self._validate_args:
self._validate_sample(value)
z = (value - self.loc) / self.scale
return z.exp().atan().mul(2 / math.pi)
[docs] def icdf(self, value):
return value.mul(math.pi / 2).tan().log().mul(self.scale).add(self.loc)
@property
def mean(self):
return self.loc
@property
def variance(self):
return (math.pi / 2 * self.scale) ** 2