AI Navigate
インサイト最新記事一覧AI大全

The Geometry of Efficient Nonconvex Sampling

arXiv stat.ML / 3/27/2026

💬 OpinionIdeas & Deep AnalysisModels & Research
Read original →
共有:

Key Points

  • The paper introduces a polynomial-time algorithm for uniformly sampling from an arbitrary compact set in high-dimensional space, starting from a “warm start.”
  • It establishes conditions based on isoperimetry and a natural volume-growth property that enable efficient nonconvex sampling.
  • The theoretical guarantees are positioned as a broad unification, generalizing earlier sampling results known for convex and star-shaped bodies.
  • The algorithm’s complexity depends on the dimension, the Poincaré constant of the uniform distribution over the set, and the set’s volume growth constant.
  • The work focuses on mathematical foundations for efficient sampling in nonconvex geometry, which can support downstream probabilistic inference and optimization methods.

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 Poincar\'e constant of the uniform distribution on \mathcal{X} and the volume growth constant of the set \mathcal{X}.

関連おすすめサービス

※当サイトはアフィリエイト広告を利用しています
🎧

Notta搭載AI議事録イヤホン ZENCHORD1

AI時代の仕事術。Notta搭載で会議の議事録を自動生成するスマートイヤホン。

🎙️

AI搭載ボイスレコーダー Plaud

世界100万人が愛用。AIで文字起こし・要約を自動化するボイスレコーダー。

🖼️

画像高画質化AIツール Aiarty Image Enhancer

AIで画像を高画質化。写真・イラストを簡単にアップスケール。