Robust, Accurate Stochastic Optimization for Variational Inference

Akash Dhaka, Alejandro Catalina Feliu, Michael Andersen, Måns Magnusson, Jonathan Huggins, Aki Vehtari

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

We consider the problem of fitting variational posterior approximations using
stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior distribution, (2) the choice of divergence, and (3) the optimization of the variational objective. We show that even in the best-case scenario when the exact posterior belongs to the assumed variational family, common stochastic optimization methods lead to poor variational approximations if the problem dimension is moderately large. We also demonstrate that these methods are not robust across diverse model types. Motivated by these findings, we develop a more robust and accurate stochastic optimization framework by viewing the underlying optimization algorithm as producing a Markov chain. Our approach is theoretically motivated and includes a diagnostic for convergence and a novel stopping rule, both of which are robust to
noisy evaluations of the objective function. We show empirically that the proposed framework works well on a diverse set of models: it can automatically detect stochastic optimization failure or inaccurate variational approximation.
Original languageEnglish
Title of host publicationThirty-fourth Conference on Neural Information Processing Systems
Number of pages12
Publication statusPublished - 2020
MoE publication typeA4 Article in a conference publication
EventConference on Neural Information Processing Systems - Virtual, Vancouver, Canada
Duration: 6 Dec 202012 Dec 2020
Conference number: 34

Publication series

NameAdvances in Neural Information Processing Systems
PublisherMORGAN KAUFMANN PUBLISHERS
Volume33
ISSN (Electronic)1049-5258

Conference

ConferenceConference on Neural Information Processing Systems
Abbreviated titleNeurIPS
Country/TerritoryCanada
CityVancouver
Period06/12/202012/12/2020

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