Variational Inference with Normalizing Flows

TL;DR

This paper introduces a flexible approach for variational inference using normalizing flows, enabling the approximation of complex posteriors beyond simple families, which improves inference quality and scalability.

Contribution

It proposes a novel method employing normalizing flows to construct arbitrarily complex and scalable approximate posteriors in variational inference.

Findings

Normalizing flows significantly improve posterior approximation quality.

The approach enhances scalability and applicability of variational inference.

Empirical results show better performance over traditional methods.

Abstract

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.