# 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 torch.distributions import Transform
from pyro.distributions.conditional import ConditionalTransformModule
from pyro.distributions.torch_transform import TransformModule
from pyro.distributions.util import copy_docs_from
from pyro.nn import DenseNN
@copy_docs_from(Transform)
class ConditionedRadial(Transform):
domain = constraints.real
codomain = constraints.real
bijective = True
event_dim = 1
def __init__(self, x0=None, alpha_prime=None, beta_prime=None):
super().__init__(cache_size=1)
self.x0 = x0
self.alpha_prime = alpha_prime
self.beta_prime = beta_prime
self._cached_logDetJ = None
# This method ensures that torch(u_hat, w) > -1, required for invertibility
def u_hat(self, u, w):
alpha = torch.matmul(u.unsqueeze(-2), w.unsqueeze(-1)).squeeze(-1)
a_prime = -1 + F.softplus(alpha)
return u + (a_prime - alpha) * w.div(w.pow(2).sum(dim=-1, keepdim=True))
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.x0.size(-1) - 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("ConditionedRadial object expected to find key in intermediates cache but didn't")
def log_abs_det_jacobian(self, x, y):
"""
Calculates the elementwise determinant of the log Jacobian
"""
x_old, y_old = self._cached_x_y
if x is not x_old or y is not y_old:
# This call to the parent class Transform will update the cache
# as well as calling self._call and recalculating y and log_detJ
self(x)
return self._cached_logDetJ
[docs]@copy_docs_from(ConditionedRadial)
class Radial(ConditionedRadial, 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
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:
[1] Danilo Jimenez Rezende, Shakir Mohamed. Variational Inference with
Normalizing Flows. [arXiv:1505.05770]
"""
domain = constraints.real
codomain = constraints.real
bijective = True
event_dim = 1
def __init__(self, input_dim):
super().__init__()
self.x0 = nn.Parameter(torch.Tensor(input_dim,))
self.alpha_prime = nn.Parameter(torch.Tensor(1,))
self.beta_prime = nn.Parameter(torch.Tensor(1,))
self.input_dim = input_dim
self.reset_parameters()
[docs] def reset_parameters(self):
stdv = 1. / math.sqrt(self.x0.size(0))
self.alpha_prime.data.uniform_(-stdv, stdv)
self.beta_prime.data.uniform_(-stdv, stdv)
self.x0.data.uniform_(-stdv, stdv)
[docs]@copy_docs_from(ConditionalTransformModule)
class ConditionalRadial(ConditionalTransformModule):
domain = constraints.real
codomain = constraints.real
bijective = True
event_dim = 1
def __init__(self, nn):
super().__init__()
self.nn = nn
[docs] def condition(self, context):
x0, alpha_prime, beta_prime = self.nn(context)
return ConditionedRadial(x0, alpha_prime, beta_prime)
[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)
[docs]def conditional_radial(input_dim, context_dim, hidden_dims=None):
"""
A helper function to create a
:class:`~pyro.distributions.transforms.ConditionalRadial` object that takes care
of constructing a dense network with the correct input/output dimensions.
:param input_dim: Dimension of input variable
:type input_dim: int
:param context_dim: Dimension of context variable
:type context_dim: int
:param hidden_dims: The desired hidden dimensions of the dense network. Defaults
to using [input_dim * 10, input_dim * 10]
:type hidden_dims: list[int]
"""
if hidden_dims is None:
hidden_dims = [input_dim * 10, input_dim * 10]
nn = DenseNN(context_dim, hidden_dims, param_dims=[input_dim, 1, 1])
return ConditionalRadial(nn)