Unbiased Implicit Variational Inference

TL;DR

The paper introduces Unbiased Implicit Variational Inference (UIVI), a novel method that employs flexible neural network-based implicit distributions to directly optimize the ELBO, resulting in improved inference quality and predictive performance.

Contribution

UIVI is the first approach to directly optimize the ELBO with an implicit variational distribution, expanding variational inference's applicability with neural network flexibility.

Findings

UIVI achieves tighter ELBOs than existing methods.

UIVI demonstrates better predictive accuracy on tested models.

UIVI maintains similar computational costs to prior approaches.

Abstract

We develop unbiased implicit variational inference (UIVI), a method that expands the applicability of variational inference by defining an expressive variational family. UIVI considers an implicit variational distribution obtained in a hierarchical manner using a simple reparameterizable distribution whose variational parameters are defined by arbitrarily flexible deep neural networks. Unlike previous works, UIVI directly optimizes the evidence lower bound (ELBO) rather than an approximation to the ELBO. We demonstrate UIVI on several models, including Bayesian multinomial logistic regression and variational autoencoders, and show that UIVI achieves both tighter ELBO and better predictive performance than existing approaches at a similar computational cost.