layer_autoregressive_transform {tfprobability}

An autoregressive normalizing flow layer, given a layer_autoregressive.

Description

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).

Usage

layer_autoregressive_transform(object, made, ...)

Arguments

object

What to compose the new Layer instance with. Typically a Sequential model or a Tensor (e.g., as returned by layer_input()). The return value depends on object. If object is:

• missing or NULL, the Layer instance is returned.

• a Sequential model, the model with an additional layer is returned.

• a Tensor, the output tensor from layer_instance(object) is returned.

made

A Made layer, which must output two parameters for each input.

...

Additional parameters passed to Keras Layer.

Details

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).

Value

a Keras layer

References

Papamakarios et al. (2017)

See Also

tfb_masked_autoregressive_flow() and layer_autoregressive()