提出新算法，显著提升对数凹函数采样、近似积分与取样精度的效率。
Sampling and Integration of Logconcave Functions by Algorithmic Diffusion
- 基于算法化扩散方法，改进了对数凹函数采样机制。
- 首次在近20年中实现三类问题的复杂度突破，逼近凸体均匀分布最优水平。
- 适用于需要高精度依赖样本统计估计的研究者。
我们研究了任意对数凹函数的采样、取样和积分问题的复杂度。新方法首次在近二十年来对一般对数凹函数的三类问题实现了复杂度改进，并达到了凸体上均匀分布情况下的最优已知复杂度水平。对于采样问题，输出保证远强于以往方法，从而简化了基于依赖随机样本的统计估计分析。
原文摘要 · Abstract (English)
We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and matches the best-known complexities for the special case of uniform distributions on convex bodies. For the sampling problem, our output guarantees are significantly stronger than previously known, and lead to a streamlined analysis of statistical estimation based on dependent random samples.
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