Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein space


Event details

Date 06.03.2024
Hour 13:1514:15
Speaker Aram-Alexandre Pooladian (NYU)
Category Conferences - Seminars
Event Language English

We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods. Our main application is to the problem of mean-field variational inference, which seeks to approximate a distribution, called the posterior, by the closest product measure in the sense of Kullback--Leibler divergence, called the mean-field approximation. We propose a novel optimization procedure for computing the mean-field approximation, where we are able to provide concrete algorithmic guarantees under the standard assumption that the posterior is strongly log-concave and log-smooth. Joint work with Yiheng Jiang and Sinho Chewi.

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