import torch
import torch.nn as nn
from torch.distributions import constraints
from pyro.distributions.torch_transform import TransformModule
from pyro.distributions.util import copy_docs_from
from pyro.distributions.transforms.utils import clamp_preserve_gradients
from pyro.nn import AutoRegressiveNN
[docs]@copy_docs_from(TransformModule)
class AffineAutoregressive(TransformModule):
"""
An implementation of the bijective transform of Inverse Autoregressive Flow (IAF), using by default Eq (10)
from Kingma Et Al., 2016,
:math:`\\mathbf{y} = \\mu_t + \\sigma_t\\odot\\mathbf{x}`
where :math:`\\mathbf{x}` are the inputs, :math:`\\mathbf{y}` are the outputs, :math:`\\mu_t,\\sigma_t`
are calculated from an autoregressive network on :math:`\\mathbf{x}`, and :math:`\\sigma_t>0`.
If the stable keyword argument is set to True then the transformation used is,
:math:`\\mathbf{y} = \\sigma_t\\odot\\mathbf{x} + (1-\\sigma_t)\\odot\\mu_t`
where :math:`\\sigma_t` is restricted to :math:`(0,1)`. This variant of IAF is claimed by the authors to
be more numerically stable than one using Eq (10), although in practice it leads to a restriction on the
distributions that can be represented, presumably since the input is restricted to rescaling by a number
on :math:`(0,1)`.
Together with :class:`~pyro.distributions.TransformedDistribution` this provides a way to create richer
variational approximations.
Example usage:
>>> from pyro.nn import AutoRegressiveNN
>>> base_dist = dist.Normal(torch.zeros(10), torch.ones(10))
>>> transform = AffineAutoregressive(AutoRegressiveNN(10, [40]))
>>> 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 the Bijector is required when, e.g., scoring the log density of a sample with
:class:`~pyro.distributions.TransformedDistribution`. This implementation caches the inverse of the Bijector
when its forward operation is called, e.g., when sampling from
:class:`~pyro.distributions.TransformedDistribution`. However, if the cached value isn't available, either because
it was overwritten during sampling a new value or an arbitary value is being scored, it will calculate it manually.
Note that this is an operation that scales as O(D) where D is the input dimension, and so should be avoided for
large dimensional uses. So in general, it is cheap to sample from IAF and score a value that was sampled by IAF,
but expensive to score an arbitrary value.
:param autoregressive_nn: an autoregressive neural network whose forward call returns a real-valued
mean and logit-scale as a tuple
:type autoregressive_nn: nn.Module
:param log_scale_min_clip: The minimum value for clipping the log(scale) from the autoregressive NN
:type log_scale_min_clip: float
:param log_scale_max_clip: The maximum value for clipping the log(scale) from the autoregressive NN
:type log_scale_max_clip: float
:param sigmoid_bias: A term to add the logit of the input when using the stable tranform.
:type sigmoid_bias: float
:param stable: When true, uses the alternative "stable" version of the transform (see above).
:type stable: bool
References:
1. Improving Variational Inference with Inverse Autoregressive Flow [arXiv:1606.04934]
Diederik P. Kingma, Tim Salimans, Rafal Jozefowicz, Xi Chen, Ilya Sutskever, Max Welling
2. Variational Inference with Normalizing Flows [arXiv:1505.05770]
Danilo Jimenez Rezende, Shakir Mohamed
3. MADE: Masked Autoencoder for Distribution Estimation [arXiv:1502.03509]
Mathieu Germain, Karol Gregor, Iain Murray, Hugo Larochelle
"""
domain = constraints.real
codomain = constraints.real
bijective = True
event_dim = 1
autoregressive = True
def __init__(
self,
autoregressive_nn,
log_scale_min_clip=-5.,
log_scale_max_clip=3.,
sigmoid_bias=2.0,
stable=False
):
super(AffineAutoregressive, self).__init__(cache_size=1)
self.arn = autoregressive_nn
self._cached_log_scale = None
self.log_scale_min_clip = log_scale_min_clip
self.log_scale_max_clip = log_scale_max_clip
self.sigmoid = nn.Sigmoid()
self.logsigmoid = nn.LogSigmoid()
self.sigmoid_bias = sigmoid_bias
self.stable = stable
if stable:
self._call = self._call_stable
self._inverse = self._inverse_stable
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)
"""
mean, log_scale = self.arn(x)
log_scale = clamp_preserve_gradients(log_scale, self.log_scale_min_clip, self.log_scale_max_clip)
self._cached_log_scale = log_scale
scale = torch.exp(log_scale)
y = scale * x + mean
return y
def _inverse(self, y):
"""
:param y: the output of the bijection
:type y: torch.Tensor
Inverts y => x. Uses a previously cached inverse if available, otherwise performs the inversion afresh.
"""
x_size = y.size()[:-1]
perm = self.arn.permutation
input_dim = y.size(-1)
x = [torch.zeros(x_size, device=y.device)] * input_dim
# NOTE: Inversion is an expensive operation that scales in the dimension of the input
for idx in perm:
mean, log_scale = self.arn(torch.stack(x, dim=-1))
inverse_scale = torch.exp(-clamp_preserve_gradients(
log_scale[..., idx], min=self.log_scale_min_clip, max=self.log_scale_max_clip))
mean = mean[..., idx]
x[idx] = (y[..., idx] - mean) * inverse_scale
x = torch.stack(x, dim=-1)
log_scale = clamp_preserve_gradients(log_scale, min=self.log_scale_min_clip, max=self.log_scale_max_clip)
self._cached_log_scale = log_scale
return x
[docs] def log_abs_det_jacobian(self, x, y):
"""
Calculates the elementwise determinant of the log Jacobian
"""
if self._cached_log_scale is not None:
log_scale = self._cached_log_scale
elif not self.stable:
_, log_scale = self.arn(x)
log_scale = clamp_preserve_gradients(log_scale, self.log_scale_min_clip, self.log_scale_max_clip)
else:
_, logit_scale = self.arn(x)
log_scale = self.logsigmoid(logit_scale + self.sigmoid_bias)
return log_scale.sum(-1)
def _call_stable(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)
"""
mean, logit_scale = self.arn(x)
logit_scale = logit_scale + self.sigmoid_bias
scale = self.sigmoid(logit_scale)
log_scale = self.logsigmoid(logit_scale)
self._cached_log_scale = log_scale
y = scale * x + (1 - scale) * mean
return y
def _inverse_stable(self, y):
"""
:param y: the output of the bijection
:type y: torch.Tensor
Inverts y => x.
"""
x_size = y.size()[:-1]
perm = self.arn.permutation
input_dim = y.size(-1)
x = [torch.zeros(x_size, device=y.device)] * input_dim
# NOTE: Inversion is an expensive operation that scales in the dimension of the input
for idx in perm:
mean, logit_scale = self.arn(torch.stack(x, dim=-1))
inverse_scale = 1 + torch.exp(-logit_scale[..., idx] - self.sigmoid_bias)
x[idx] = inverse_scale * y[..., idx] + (1 - inverse_scale) * mean[..., idx]
self._cached_log_scale = inverse_scale
x = torch.stack(x, dim=-1)
return x
[docs]def affine_autoregressive(input_dim, hidden_dims=None, **kwargs):
"""
A helper function to create an :class:`~pyro.distributions.transforms.AffineAutoregressive` 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 log_scale_min_clip: The minimum value for clipping the log(scale) from the autoregressive NN
:type log_scale_min_clip: float
:param log_scale_max_clip: The maximum value for clipping the log(scale) from the autoregressive NN
:type log_scale_max_clip: float
:param sigmoid_bias: A term to add the logit of the input when using the stable tranform.
:type sigmoid_bias: float
:param stable: When true, uses the alternative "stable" version of the transform (see above).
:type stable: bool
"""
if hidden_dims is None:
hidden_dims = [3 * input_dim + 1]
arn = AutoRegressiveNN(input_dim, hidden_dims)
return AffineAutoregressive(arn, **kwargs)