Source code for pyro.distributions.transforms.naf

import math

import torch
import torch.nn as nn
from pyro.distributions.torch_transform import TransformModule
from torch.distributions import constraints
import torch.nn.functional as F

from pyro.distributions.util import copy_docs_from

eps = 1e-8

class ELUMixin(object):
@staticmethod
def f(x):
"""
Implements the nonlinearity of NAF, in this case ELU
"""
return F.elu(x)

@staticmethod
def f_inv(x):
"""
Implements the inverse of ELU
"""
return torch.max(x, torch.zeros_like(x)) + torch.min(torch.log1p(x + eps), torch.zeros_like(x))

@staticmethod
def log_df_dx(x):
"""
Implements the log derivative of NAF nonlinearity
"""
return -F.relu(-x)

@staticmethod
def log_df_inv_dx(x):
"""
Implements the log derivative of inverse NAF nonlinearity
"""
return F.relu(-torch.log1p(x + eps))

class LeakyReLUMixin(object):
@staticmethod
def f(x):
"""
Implements the nonlinearity of NAF, in this case leaky ReLU
"""
return F.leaky_relu(x)

@staticmethod
def f_inv(x):
"""
Implements the inverse of leaky ReLU
"""
# slope for negative part is inverse of slope for positive part in f(x)
return F.leaky_relu(x, negative_slope=100.0)

@staticmethod
def log_df_dx(x):
"""
Implements the log derivative of NAF nonlinearity
"""
return torch.where(x >= 0., torch.zeros_like(x), torch.ones_like(x) * math.log(0.01))

@staticmethod
def log_df_inv_dx(x):
"""
Implements the log derivative of inverse NAF nonlinearity
"""
return torch.where(x >= 0., torch.zeros_like(x), torch.ones_like(x) * math.log(100.0))

class SigmoidalMixin(object):
@staticmethod
def f(x):
"""
Implements the nonlinearity of NAF, in this case sigmoid with scaled output
"""
return torch.sigmoid(x) * (1. - eps) + 0.5 * eps

@staticmethod
def f_inv(x):
"""
Implements the inverse scaled sigmoid nonlinearity
"""
y = (x - 0.5 * eps) / (1. - eps)

@staticmethod
def log_df_dx(x):
"""
Implements the log derivative of scaled sigmoid nonlinearity
"""
return F.logsigmoid(x) + F.logsigmoid(-x) + torch.log1p(torch.tensor(-eps))

@staticmethod
def log_df_inv_dx(x):
"""
Implements the log derivative of inverse scaled sigmoid nonlinearity
"""
y = (x - 0.5 * eps) / (1. - eps)
return -torch.log(y + eps) - torch.log(1. - y) - math.log(1. - eps)

class TanhMixin(object):
@staticmethod
def f(x):
"""
The nonlinearity to apply after each masked block linear layer
"""

@staticmethod
def log_df_dx(x):
return - 2. * (x - math.log(2.) + F.softplus(- 2. * x))

@copy_docs_from(TransformModule)
class DeepNAFFlow(TransformModule):
domain = constraints.real
codomain = constraints.real
bijective = True
event_dim = 1
autoregressive = True

def __init__(self, autoregressive_nn, hidden_units=16):
super(DeepNAFFlow, self).__init__(cache_size=1)
self.arn = autoregressive_nn
self.hidden_units = hidden_units
self.logsoftmax = nn.LogSoftmax(dim=-2)
self._cached_A = None
self._cached_W_pre = None
self._cached_C = None
self._cached_D = 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 TransformedDistribution x is a
sample from the base distribution (or the output of a previous flow)
"""
# A, W, b ~ batch_shape x hidden_units x event_shape
A, W_pre, b = self.arn(x)

# 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)
D = (W * self.f(C)).sum(dim=-2)
y = self.f_inv(D)

self._cached_A = A
self._cached_W_pre = W_pre
self._cached_C = C
self._cached_D = D

return y

# This method returns log(abs(det(dy/dx)), which is equal to -log(abs(det(dx/dy))
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
D = self._cached_D

log_dydD = self.log_df_inv_dx(D)
log_dDdx = torch.logsumexp(torch.log(A + eps) + self.logsoftmax(W_pre) + self.log_df_dx(C), dim=-2)
log_det = log_dydD + log_dDdx
return log_det.sum(-1)

@staticmethod
def f(x):
"""
Implements the nonlinearity of NAF
"""
raise NotImplementedError

@staticmethod
def f_inv(x):
"""
Implements the inverse of the NAF nonlinearity
"""
raise NotImplementedError

@staticmethod
def log_df_dx(x):
"""
Implements the log derivative of NAF nonlinearity
"""
raise NotImplementedError

@staticmethod
def log_df_inv_dx(x):
"""
Implements the log derivative of inverse NAF nonlinearity
"""
raise NotImplementedError

[docs]@copy_docs_from(TransformModule) class DeepELUFlow(ELUMixin, DeepNAFFlow): """ An implementation of deep ELU flow (DSF) Neural Autoregressive Flow (NAF), of the "IAF flavour" that can be used for sampling and scoring samples drawn from it (but not arbitrary ones). This flow is suggested in Huang et al., 2018, section 3.3, but left for future experiments. Example usage: >>> from pyro.nn import AutoRegressiveNN >>> base_dist = dist.Normal(torch.zeros(10), torch.ones(10)) >>> arn = AutoRegressiveNN(10, , param_dims=*3) >>> naf = DeepELUFlow(arn, hidden_units=16) >>> pyro.module("my_naf", naf) # doctest: +SKIP >>> naf_dist = dist.TransformedDistribution(base_dist, [naf]) >>> naf_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 Reference: Neural Autoregressive Flows [arXiv:1804.00779] Chin-Wei Huang, David Krueger, Alexandre Lacoste, Aaron Courville """ pass
[docs]@copy_docs_from(TransformModule) class DeepSigmoidalFlow(SigmoidalMixin, DeepNAFFlow): """ An implementation of deep sigmoidal flow (DSF) Neural Autoregressive Flow (NAF), 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, , param_dims=*3) >>> naf = DeepSigmoidalFlow(arn, hidden_units=16) >>> pyro.module("my_naf", naf) # doctest: +SKIP >>> naf_dist = dist.TransformedDistribution(base_dist, [naf]) >>> naf_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 Reference: Neural Autoregressive Flows [arXiv:1804.00779] Chin-Wei Huang, David Krueger, Alexandre Lacoste, Aaron Courville """ pass
[docs]@copy_docs_from(TransformModule) class DeepLeakyReLUFlow(LeakyReLUMixin, DeepNAFFlow): """ An implementation of deep leaky ReLU flow (DSF) Neural Autoregressive Flow (NAF), of the "IAF flavour" that can be used for sampling and scoring samples drawn from it (but not arbitrary ones). This flow is suggested in Huang et al., 2018, section 3.3, but left for future experiments. Example usage: >>> from pyro.nn import AutoRegressiveNN >>> base_dist = dist.Normal(torch.zeros(10), torch.ones(10)) >>> arn = AutoRegressiveNN(10, , param_dims=*3) >>> naf = DeepLeakyReLUFlow(arn, hidden_units=16) >>> pyro.module("my_naf", naf) # doctest: +SKIP >>> naf_dist = dist.TransformedDistribution(base_dist, [naf]) >>> naf_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 Reference: Neural Autoregressive Flows [arXiv:1804.00779] Chin-Wei Huang, David Krueger, Alexandre Lacoste, Aaron Courville """ pass