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
tensor([-0.4071, -0.5030, 0.7924, -0.2366, -0.2387, -0.1417, 0.0868,
0.1389, -0.4629, 0.0986])
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:
Neural Autoregressive Flows [arXiv:1804.00779]
Chin-Wei Huang, David Krueger, Alexandre Lacoste, Aaron Courville
"""
domain = constraints.real
codomain = constraints.real
bijective = True
event_dim = 1
def __init__(self, autoregressive_nn, hidden_units=16, activation='sigmoid'):
super(NeuralAutoregressive, self).__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)