In-and-Out: Algorithmic Diffusion for Sampling Convex Bodies
- URL: http://arxiv.org/abs/2405.01425v2
- Date: Wed, 20 Nov 2024 19:01:42 GMT
- Title: In-and-Out: Algorithmic Diffusion for Sampling Convex Bodies
- Authors: Yunbum Kook, Santosh S. Vempala, Matthew S. Zhang,
- Abstract summary: We present a new random walk for uniformly sampling high-dimensional convex bodies.
It achieves state-of-the-art runtime complexity with stronger guarantees on the output.
- Score: 7.70133333709347
- License:
- Abstract: We present a new random walk for uniformly sampling high-dimensional convex bodies. It achieves state-of-the-art runtime complexity with stronger guarantees on the output than previously known, namely in R\'enyi divergence (which implies TV, $\mathcal{W}_2$, KL, $\chi^2$). The proof departs from known approaches for polytime algorithms for the problem -- we utilize a stochastic diffusion perspective to show contraction to the target distribution with the rate of convergence determined by functional isoperimetric constants of the stationary density.
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