An autoregressive normalizing flow layer, given a layer_autoregressive.
Following Papamakarios et al. (2017), given an autoregressive model p(x) with conditional distributions in the location-scale family, we can construct a normalizing flow for p(x).
layer_autoregressive_transform(object, made, ...)
object |
Model or layer object |
made |
A |
... |
Additional parameters passed to Keras Layer. |
Specifically, suppose made is a [layer_autoregressive()] – a layer implementing
a Masked Autoencoder for Distribution Estimation (MADE) – that computes location
and log-scale parameters made(x)[i] for each input x[i]. Then we can represent
the autoregressive model p(x) as x = f(u) where u is drawn
from from some base distribution and where f is an invertible and
differentiable function (i.e., a Bijector) and f^{-1}(x) is defined by:
library(tensorflow)
library(zeallot)
f_inverse <- function(x) {
c(shift, log_scale) %<-% tf$unstack(made(x), 2, axis = -1L)
(x - shift) * tf$math$exp(-log_scale)
}Given a layer_autoregressive() made, a layer_autoregressive_transform()
transforms an input tfd_* p(u) to an output tfd_* p(x) where
x = f(u).
a Keras layer
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