Source code for pyro.distributions.softlaplace

# 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