Challenges for BBVI with Normalizing Flows

Akash Kumar Dhaka, Alejandro Catalina, Manushi Welandawe, Michael Riis Andersen, Jonathan H. Huggins, Aki Vehtari

Keywords: BBVI, Variational Inference, Importance Sampling, Normalizing Flows, Pre-asymptotics, Stochastic Optimisation

TL;DR: Black box variational inference (BBVI) is hard. We develop a conceptual and experimental framework for assessing the reliability of BBVI and give a set of recommendations for using Normalizing Flows as the approximating family..

Abstract: Current black-box variational inference (BBVI) methods require the user to make numerous design choices---such as the selection of variational objective and approximating family---yet there is little principled guidance on how to do so. We develop a conceptual framework and set of experimental tools to understand the effects of these choices, which we leverage to propose best practices for maximizing posterior approximation accuracy. Our approach is based on studying the pre-asymptotic tail behavior of the density ratios between the joint distribution and the variational approximation, then exploiting insights and tools from the importance sampling literature. We focus on normalizing flow models and give recommendations on how to be used(and diagnostics) in BBVI, though we are not limited to them.

Questions/feedback Request For Reviewers: Any feedback is welcome. The conceptual framework and ideas we give in this paper are generally applicable to all approximating families and not just normalizing flows but we also give recommendations for using them more effectively in BBVI context.