Bayes Reading Group: Aram-Alexandre Pooladian ( NYU)

Friday Nov 8, 2024, 11:00 AM → 12:00 PM America/New_York

3rd Floor Conference Room (162 Fifth Avenue )

Discussion Lead: Aram-Alexandre Pooladian (NYU)

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

Link: https://arxiv.org/abs/2312.02849

Abstract: 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 $\pi$ over $\text{Undefined control sequence R}$ by a product measure ${\pi }^{\star }$.

When $\pi$ is strongly log-concave and log-smooth, we provide (1) approximation rates certifying that ${\pi }^{\star }$ is close to the minimizer ${\pi }_{\diamond }^{\star }$ of the KL divergence over a \emph{polyhedral} set $\text{Undefined control sequence Pdiam}$, and (2) an algorithm for minimizing $\text{Undefined control sequence kl}$ over $\text{Undefined control sequence Pdiam}$ with accelerated complexity $O(\sqrt{\kappa }\log (\kappa d/{\epsilon }^2))$, where $\kappa$ is the condition number of $\pi$.