2 min read

Variational Inference with Normalizing Flows

On Tuesday \(28^{\text{th}}\) of July, Mauro presented Variational Inference with Normalizing Flows by Rezende and Mohamed. Two good review papers are Normalizing Flows for Probabilistic Modeling and Inference, which is more Tutorial in nature, and Normalizing Flows: An Introduction and Review of Current Methods, which is a bit more technical. Slides for the talk are available here.

The abstract is given below:

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