Year: 2026
Type: preprint
Abstract: We present an efficient algorithm for uniformly sampling from an arbitrary compact body $\mathcal{X} \subset \mathbb{R}^n$ from a warm start under isoperimetry and a natural volume growth condition. Our result provides a substantial common generalization of known results for convex bodies and star-shaped bodies. The complexity of the algorithm is polynomial in the dimension, the Poincaré constant of the uniform distribution on $\mathcal{X}$ and the volume growth constant of the set $\mathcal{X}$.
Source: arXiv (Cornell University)
Authors: Vempala, Santosh S., Wibisono, Andre
Institutions: Georgia Institute of Technology, Yale University
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Awards: CAREER: A Rigorous Translation of Continuous-Time Dynamics to Discrete-Time Algorithms: Optimization, Sampling, and Machine Learning, Collaborative Research: AF: Medium: Fundamental Challenges in Discrete and Continuous Optimization, Collaborative Research: CIF: Medium: An Algorithmic Theory of Hamiltonian Dynamics for Sampling, Optimization, and Games, G6671297155
OpenAlex ID: W7141297784
Cites:
Cited by:
Related to: