混合切片采样的最优切片自适应调优
Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling
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中文总结 AI 辅助
本文分析混合切片采样的计算成本，提出自动切片自适应调优方案，具有次优性界限和收敛保证，模拟显示其性能近乎最优且不依赖初始参数。
中文摘要 AI 辅助
切片采样是一种马尔可夫链蒙特卡洛算法，每次迭代从目标密度函数的“切片”（即超水平集）中均匀抽取下一个状态，从而自动适应当地目标尺度。在实际中，精确的切片是未知的，因此通用实现使用从长度为$w>0$的起始区间扩展的近似切片，其计算成本取决于$w$。本文针对具有连续切片的目标，分析了混合切片采样在不同切片查找方案下，每迭代平均目标密度评估次数作为$w$的函数。论文利用分析结果开发了自动的切片自适应调优方案，并提供了次优性界限和渐近收敛保证。模拟表明，该调优方案能可靠地产生近乎最优的切片自适应调优，且基本不依赖于$w$的初始设置。
英文摘要
Slice sampling is a Markov chain Monte Carlo algorithm that draws its next state uniformly from a "slice"---a super-level set of the target density function---at each iteration, thereby providing automatic local adaptivity to the scale of the target. In practice the exact slice is not known, so general-purpose implementations use an approximate slice that is grown from a starting interval of length $w>0$, with a computational cost that depends on $w$. This work presents an analysis of the average per-iteration number of target density evaluations, as a function of $w$, of hybrid slice sampling with various slice-finding schemes for targets with contiguous slices. The paper uses the results of the analysis to develop automated, slice-adaptive tuning schemes along with suboptimality bounds and asymptotic convergence guarantees. Simulations demonstrate that the tuning schemes reliably yield near-optimal slice-adaptive tuning with essentially no dependence on the initial setting of $w$.
发表机构
- UBC（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。
