2024-06-30-jiang24a.md

title	section	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein space	Original Papers	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 $\mathbb{R}^d$ 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 $\pi^\star_\diamond$ of the KL divergence over a \emph{polyhedral} set $\mathcal{P}_\diamond$, and (2) an algorithm for minimizing $\text{KL}(\cdot\|\pi)$ over $\mathcal{P}_\diamond$ with accelerated complexity $O(\sqrt \kappa \log(\kappa d/\varepsilon^2))$, where $\kappa$ is the condition number of $\pi$.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	jiang24a	0	Algorithms for mean-field variational inference via polyhedral optimization in the {W}asserstein space	2720	2721	2720-2721	2720	false	Jiang, Yiheng and Chewi, Sinho and Pooladian, Aram-Alexandre	given family Yiheng Jiang given family Sinho Chewi given family Aram-Alexandre Pooladian	2024-06-30		Proceedings of Thirty Seventh Conference on Learning Theory	247	inproceedings	date-parts 2024 6 30	https://proceedings.mlr.press/v247/jiang24a/jiang24a.pdf