Note on the equivalence of hierarchical variational models and auxiliary deep generative models

TL;DR

This paper demonstrates that hierarchical variational models and auxiliary deep generative models, two approaches for flexible variational posteriors, are mathematically equivalent, unifying their theoretical understanding.

Contribution

It establishes the equivalence between hierarchical variational models and auxiliary deep generative models, clarifying their relationship in variational inference.

Findings

The two methods are mathematically equivalent.

This equivalence unifies different approaches in variational inference.

Provides theoretical insight into model construction.

Abstract

This note compares two recently published machine learning methods for constructing flexible, but tractable families of variational hidden-variable posteriors. The first method, called "hierarchical variational models" enriches the inference model with an extra variable, while the other, called "auxiliary deep generative models", enriches the generative model instead. We conclude that the two methods are mathematically equivalent.