Generalized Transformation-based Gradient

TL;DR

This paper generalizes the reparameterization trick in variational inference by allowing arbitrary transformations, enabling broader applicability beyond distributions with tractable inverse CDFs, and combines it with control variates for improved variance reduction.

Contribution

It introduces a generalized reparameterization method using arbitrary transformations, extending the scope of variational inference techniques and integrating control variates for better performance.

Findings

The generalized transformation broadens the class of distributions for reparameterization.

The proposed model is a special case of control variates, combining their benefits.

Potential for improved variance reduction in variational inference.

Abstract

The reparameterization trick has become one of the most useful tools in the field of variational inference. However, the reparameterization trick is based on the standardization transformation which restricts the scope of application of this method to distributions that have tractable inverse cumulative distribution functions or are expressible as deterministic transformations of such distributions. In this paper, we generalized the reparameterization trick by allowing a general transformation. We discover that the proposed model is a special case of control variate indicating that the proposed model can combine the advantages of CV and generalized reparameterization.