# Source code for pyro.distributions.transforms.neural_autoregressive

# Copyright (c) 2017-2019 Uber Technologies, Inc.

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]class ELUTransform(Transform): r""" Bijective transform via the mapping :math:y = \text{ELU}(x). """ domain = constraints.real codomain = constraints.positive bijective = True sign = +1 def __eq__(self, other): return isinstance(other, ELUTransform) def _call(self, x): return F.elu(x) def _inverse(self, y): return torch.max(y, torch.zeros_like(y)) + torch.min(torch.log1p(y + eps), torch.zeros_like(y))
[docs] def log_abs_det_jacobian(self, x, y): return -F.relu(-x)
[docs]def elu(): """ A helper function to create an :class:~pyro.distributions.transform.ELUTransform object for consistency with other helpers. """ return ELUTransform()
[docs]class LeakyReLUTransform(Transform): r""" Bijective transform via the mapping :math:y = \text{LeakyReLU}(x). """ domain = constraints.real codomain = constraints.positive bijective = True sign = +1 def __eq__(self, other): return isinstance(other, LeakyReLUTransform) def _call(self, x): return F.leaky_relu(x) def _inverse(self, y): return F.leaky_relu(y, negative_slope=100.0)
[docs] def log_abs_det_jacobian(self, x, y): return torch.where(x >= 0., torch.zeros_like(x), torch.ones_like(x) * math.log(0.01))
[docs]def leaky_relu(): """ A helper function to create a :class:~pyro.distributions.transforms.LeakyReLUTransform object for consistency with other helpers. """ return LeakyReLUTransform()
[docs]class TanhTransform(Transform): r""" Bijective transform via the mapping :math:y = \text{tanh}(x). """ domain = constraints.real codomain = constraints.interval(-1., 1.) bijective = True sign = +1
[docs] @staticmethod def atanh(x): return 0.5 * (x.log1p() - (-x).log1p())
def __eq__(self, other): return isinstance(other, TanhTransform) def _call(self, x): return torch.tanh(x) def _inverse(self, y): eps = torch.finfo(y.dtype).eps return self.atanh(y.clamp(min=-1. + eps, max=1. - eps))
[docs] def log_abs_det_jacobian(self, x, y): return - 2. * (x - math.log(2.) + F.softplus(- 2. * x))
[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().__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)