提出首个多项式复杂度采样算法，可高效从多峰分布中采样。
Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusion
- 通过反向扩散过程与自归一化蒙特卡洛估计实现采样
- 在固定维度下，查询复杂度为多峰参数的多项式级
- 无需先验模式位置信息，适用于一般高斯混合模型
即使在低维情形下，从多峰分布中采样仍具挑战性。本文针对一类广泛分布（包括所有高斯混合模型）提出了首个采样算法，其查询复杂度在固定维度下为多峰参数的多项式级别。该算法模拟时间反向扩散过程，采用中间得分函数的自归一化蒙特卡洛估计。与以往工作不同，该方法避免了弛豫现象，无需预先知道模式位置，且放宽了长期存在的对数光滑性假设，从而首次覆盖了一般高斯混合模型。
原文摘要 · Abstract (English)
Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in the parameters governing multi-modality, assuming fixed dimension. Our sampling algorithm simulates a time-reversed diffusion process, using a self-normalized Monte Carlo estimator of the intermediate score functions. Unlike previous works, it avoids metastability, requires no prior knowledge of the mode locations, and relaxes the well-known log-smoothness assumption which excluded general Gaussian mixtures so far.
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