An optimization perspective on log-concave sampling and beyond
Name
chewi-schewi-phd-math-2023-thesis-pdf.pdf
Description
Thesis PDF
Size
6.54 MB
Format
Adobe PDF
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e68e579167e81be273b180cf2e20dd45
Author(s)
Chewi, Sinho
Advisor(s)
Rigollet, Philippe
Date Issued
June 2023
Publisher
Massachusetts Institute of Technology
Abstract
The primary contribution of this thesis is to advance the theory of complexity for sampling from a continuous probability density over R^d. Some highlights include: a new analysis of the proximal sampler, taking inspiration from the proximal point algorithm in optimization; an improved and sharp analysis of the Metropolis-adjusted Langevin algorithm, yielding new state-of-the-art guarantees for high-accuracy log-concave sampling; the first lower bounds for the complexity of log-concave sampling; an analysis of mirror Langevin Monte Carlo for constrained sampling; and the development of a theory of approximate first-order stationarity in non-log-concave sampling.
We further illustrate the main tools in this work—diffusions and Wasserstein gradient flows—through applications to functional inequalities, the entropic barrier, Wasserstein barycenters, variational inference, and diffusion models.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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