The Geometry of Efficient Nonconvex Sampling
Data Structures and Algorithms
2026-03-27 v1 Machine Learning
Statistics Theory
Machine Learning
Statistics Theory
Abstract
We present an efficient algorithm for uniformly sampling from an arbitrary compact body 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 Poincar\'e constant of the uniform distribution on and the volume growth constant of the set .
Cite
@article{arxiv.2603.25622,
title = {The Geometry of Efficient Nonconvex Sampling},
author = {Santosh S. Vempala and Andre Wibisono},
journal= {arXiv preprint arXiv:2603.25622},
year = {2026}
}