Dates
Thursday, January 23, 2020 - 11:00am to Thursday, January 23, 2020 - 12:00pm
Location
SCGP 313
Event Description

TITLE: Sampling Using Langevin Diffusions Beyond the Worst-Case by
Andrej Risteski of CMU

ABSTRACT: Many tasks involving generative models involve being able to sample from distributions parametrized as p(x) = e^{-f(x)}/Z where Z is the normalizing constant, for some function f whose values and gradients we can query. This mode of access to f is natural -- for instance sampling from posteriors in latent-variable models. Classical results show that a natural random walk, Langevin diffusion, mixes rapidly when f is convex. Unfortunately, even in simple examples, the applications listed above will entail working with functions f that are nonconvex.

We exhibit instances where Langevin diffusion (combined with other tools) can provably be shown to mix rapidly in instances of relevance in practice: distributions p that are multimodal, as well as distributions p that have a natural manifold structure on their level sets.

Event Title
Talk: Sampling Using Langevin Diffusions Beyond the Worst-Case by Andrej Risteski