Source code for pyro.distributions.transforms.radial

# Copyright (c) 2017-2019 Uber Technologies, Inc.
# SPDX-License-Identifier: Apache-2.0

import math

import torch
import torch.nn as nn
from torch.distributions import constraints
import torch.nn.functional as F

from pyro.distributions.torch_transform import TransformModule
from pyro.distributions.util import copy_docs_from

[docs]@copy_docs_from(TransformModule) class Radial(TransformModule): """ A 'radial' bijective transform using the equation, :math:`\\mathbf{y} = \\mathbf{x} + \\beta h(\\alpha,r)(\\mathbf{x} - \\mathbf{x}_0)` where :math:`\\mathbf{x}` are the inputs, :math:`\\mathbf{y}` are the outputs, and the learnable parameters are :math:`\\alpha\\in\\mathbb{R}^+`, :math:`\\beta\\in\\mathbb{R}`, :math:`\\mathbf{x}_0\\in\\mathbb{R}^D`, for input dimension :math:`D`, :math:`r=||\\mathbf{x}-\\mathbf{x}_0||_2`, :math:`h(\\alpha,r)=1/(\\alpha+r)`. For this to be an invertible transformation, the condition :math:`\\beta>-\\alpha` is enforced. Together with :class:`~pyro.distributions.TransformedDistribution` this provides a way to create richer variational approximations. Example usage: >>> base_dist = dist.Normal(torch.zeros(10), torch.ones(10)) >>> transform = Radial(10) >>> pyro.module("my_transform", transform) # doctest: +SKIP >>> flow_dist = dist.TransformedDistribution(base_dist, [transform]) >>> flow_dist.sample() # doctest: +SKIP tensor([-0.4071, -0.5030, 0.7924, -0.2366, -0.2387, -0.1417, 0.0868, 0.1389, -0.4629, 0.0986]) The inverse of this transform does not possess an analytical solution and is left unimplemented. However, the inverse is cached when the forward operation is called during sampling, and so samples drawn using the radial transform can be scored. :param input_dim: the dimension of the input (and output) variable. :type input_dim: int References: Variational Inference with Normalizing Flows [arXiv:1505.05770] Danilo Jimenez Rezende, Shakir Mohamed """ domain = constraints.real codomain = constraints.real bijective = True event_dim = 1 def __init__(self, input_dim): super().__init__(cache_size=1) self.input_dim = input_dim self._cached_logDetJ = None self.x0 = nn.Parameter(torch.Tensor(input_dim)) # These are the unconstrained parameters self.alpha_prime = nn.Parameter(torch.Tensor(1)) self.beta_prime = nn.Parameter(torch.Tensor(1)) self.reset_parameters()
[docs] def reset_parameters(self): stdv = 1. / math.sqrt(self.x0.size(0)), stdv), stdv), stdv)
def _call(self, x): """ :param x: the input into the bijection :type x: torch.Tensor Invokes the bijection x=>y; in the prototypical context of a :class:`~pyro.distributions.TransformedDistribution` `x` is a sample from the base distribution (or the output of a previous transform) """ # Ensure invertibility using approach in appendix A.2 alpha = F.softplus(self.alpha_prime) beta = -alpha + F.softplus(self.beta_prime) # Compute y and logDet using Equation 14. diff = x - self.x0 r = diff.norm(dim=-1, keepdim=True) h = (alpha + r).reciprocal() h_prime = - (h ** 2) beta_h = beta * h self._cached_logDetJ = ((self.input_dim - 1) * torch.log1p(beta_h) + torch.log1p(beta_h + beta * h_prime * r)).sum(-1) return x + beta_h * diff def _inverse(self, y): """ :param y: the output of the bijection :type y: torch.Tensor Inverts y => x. As noted above, this implementation is incapable of inverting arbitrary values `y`; rather it assumes `y` is the result of a previously computed application of the bijector to some `x` (which was cached on the forward call) """ raise KeyError("Radial object expected to find key in intermediates cache but didn't")
[docs] def log_abs_det_jacobian(self, x, y): """ Calculates the elementwise determinant of the log Jacobian """ return self._cached_logDetJ
[docs]def radial(input_dim): """ A helper function to create a :class:`~pyro.distributions.transforms.Radial` object for consistency with other helpers. :param input_dim: Dimension of input variable :type input_dim: int """ return Radial(input_dim)