# Copyright (c) 2017-2019 Uber Technologies, Inc.
# SPDX-License-Identifier: Apache-2.0
from __future__ import absolute_import, division, print_function
import math
import torch
import torch.nn as nn
from pyro.distributions.torch_transform import TransformModule
from torch.distributions import constraints
from torch.distributions.transforms import Transform, SigmoidTransform
import torch.nn.functional as F
from pyro.distributions.util import copy_docs_from
from pyro.nn import AutoRegressiveNN
eps = 1e-8
[docs]def elu():
"""
A helper function to create an
:class:`~pyro.distributions.transform.ELUTransform` object for consistency with
other helpers.
"""
return ELUTransform()
[docs]def leaky_relu():
"""
A helper function to create a
:class:`~pyro.distributions.transforms.LeakyReLUTransform` object for
consistency with other helpers.
"""
return LeakyReLUTransform()
[docs]def tanh():
"""
A helper function to create a
:class:`~pyro.distributions.transforms.TanhTransform` object for consistency
with other helpers.
"""
return TanhTransform()
[docs]@copy_docs_from(TransformModule)
class NeuralAutoregressive(TransformModule):
"""
An implementation of the deep Neural Autoregressive Flow (NAF) bijective
transform of the "IAF flavour" that can be used for sampling and scoring samples
drawn from it (but not arbitrary ones).
Example usage:
>>> from pyro.nn import AutoRegressiveNN
>>> base_dist = dist.Normal(torch.zeros(10), torch.ones(10))
>>> arn = AutoRegressiveNN(10, [40], param_dims=[16]*3)
>>> transform = NeuralAutoregressive(arn, hidden_units=16)
>>> pyro.module("my_transform", transform) # doctest: +SKIP
>>> flow_dist = dist.TransformedDistribution(base_dist, [transform])
>>> flow_dist.sample() # doctest: +SKIP
The inverse operation is not implemented. This would require numerical
inversion, e.g., using a root finding method - a possibility for a future
implementation.
:param autoregressive_nn: an autoregressive neural network whose forward call
returns a tuple of three real-valued tensors, whose last dimension is the
input dimension, and whose penultimate dimension is equal to hidden_units.
:type autoregressive_nn: nn.Module
:param hidden_units: the number of hidden units to use in the NAF transformation
(see Eq (8) in reference)
:type hidden_units: int
:param activation: Activation function to use. One of 'ELU', 'LeakyReLU',
'sigmoid', or 'tanh'.
:type activation: string
Reference:
[1] Chin-Wei Huang, David Krueger, Alexandre Lacoste, Aaron Courville. Neural
Autoregressive Flows. [arXiv:1804.00779]
"""
domain = constraints.real
codomain = constraints.real
bijective = True
event_dim = 1
def __init__(self, autoregressive_nn, hidden_units=16, activation='sigmoid'):
super().__init__(cache_size=1)
# Create the intermediate transform used
name_to_mixin = {
'ELU': ELUTransform,
'LeakyReLU': LeakyReLUTransform,
'sigmoid': SigmoidTransform,
'tanh': TanhTransform}
if activation not in name_to_mixin:
raise ValueError('Invalid activation function "{}"'.format(activation))
self.T = name_to_mixin[activation]()
self.arn = autoregressive_nn
self.hidden_units = hidden_units
self.logsoftmax = nn.LogSoftmax(dim=-2)
self._cached_log_df_inv_dx = None
self._cached_A = None
self._cached_W_pre = None
self._cached_C = None
self._cached_T_C = None
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)
"""
# A, W, b ~ batch_shape x hidden_units x event_shape
A, W_pre, b = self.arn(x)
T = self.T
# Divide the autoregressive output into the component activations
A = F.softplus(A)
C = A * x.unsqueeze(-2) + b
W = F.softmax(W_pre, dim=-2)
T_C = T(C)
D = (W * T_C).sum(dim=-2)
y = T.inv(D)
self._cached_log_df_inv_dx = T.inv.log_abs_det_jacobian(D, y)
self._cached_A = A
self._cached_W_pre = W_pre
self._cached_C = C
self._cached_T_C = T_C
return y
# This method returns log(abs(det(dy/dx)), which is equal to -log(abs(det(dx/dy))
[docs] def log_abs_det_jacobian(self, x, y):
"""
Calculates the elementwise determinant of the log Jacobian
"""
A = self._cached_A
W_pre = self._cached_W_pre
C = self._cached_C
T_C = self._cached_T_C
T = self.T
log_dydD = self._cached_log_df_inv_dx
log_dDdx = torch.logsumexp(torch.log(A + eps) + self.logsoftmax(W_pre) +
T.log_abs_det_jacobian(C, T_C), dim=-2)
log_det = log_dydD + log_dDdx
return log_det.sum(-1)
[docs]def neural_autoregressive(input_dim, hidden_dims=None, activation='sigmoid', width=16):
"""
A helper function to create a
:class:`~pyro.distributions.transforms.NeuralAutoregressive` object that takes
care of constructing an autoregressive network with the correct input/output
dimensions.
:param input_dim: Dimension of input variable
:type input_dim: int
:param hidden_dims: The desired hidden dimensions of the autoregressive network.
Defaults to using [3*input_dim + 1]
:type hidden_dims: list[int]
:param activation: Activation function to use. One of 'ELU', 'LeakyReLU',
'sigmoid', or 'tanh'.
:type activation: string
:param width: The width of the "multilayer perceptron" in the transform (see
paper). Defaults to 16
:type width: int
"""
if hidden_dims is None:
hidden_dims = [3 * input_dim + 1]
arn = AutoRegressiveNN(input_dim, hidden_dims, param_dims=[width] * 3)
return NeuralAutoregressive(arn, hidden_units=width, activation=activation)