Abstract
Sampling is a fundamental and arguably very important task with numerous applications in Machine Learning. One approach to sample from a high dimensional distribution e-f for some function f is the Langevin Algorithm (LA). Recently, there has been a lot of progress in showing fast convergence of LA even in cases where f is non-convex, notably Vempala and Wibisono [2019], Moitra and Risteski [2020] in which the former paper focuses on functions f defined in Rn and the latter paper focuses on functions with symmetries (like matrix completion type objectives) with manifold structure. Our work generalizes the results of Vempala and Wibisono [2019] where f is defined on a manifold M rather than Rn. From technical point of view, we show that KL decreases in a geometric rate whenever the distribution e-f satisfies a log-Sobolev inequality on M.
Original language | English (US) |
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Journal | Advances in Neural Information Processing Systems |
Volume | 2020-December |
State | Published - 2020 |
Event | 34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online Duration: Dec 6 2020 → Dec 12 2020 |
ASJC Scopus subject areas
- Computer Networks and Communications
- Information Systems
- Signal Processing