自动调整步长的马尔可夫链蒙特卡洛方法，提升复杂分布采样效率。
AutoStep: Locally adaptive involutive MCMC
- 根据目标分布局部几何自适应选择步长，无需手动调参。
- 在多个复杂分布上实现单位成本下有效样本量领先。
- 理论保证收敛性，适合高维多尺度问题采样。
许多常见的马尔可夫链蒙特卡洛（MCMC）核可通过带步长参数的确定性对合提议来表述。实践中选择合适步长常具挑战性；对于复杂的多尺度目标分布，可能不存在全局适用的步长。本文提出一种新型对合MCMC方法——AutoStep MCMC，可在每一步迭代中根据目标分布的局部几何自适应选择步长。我们证明，在温和条件下，AutoStep MCMC满足π-不变性、不可约性和非周期性，并给出了期望能量跳跃距离和每步开销的界。实验评估了所提步长选择策略的鲁棒性与有效性，结果表明，AutoStep MCMC在一系列挑战性目标分布上，单位成本下的有效样本量可媲美最先进方法。
原文摘要 · Abstract (English)
Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods -- AutoStep MCMC -- that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that under mild conditions AutoStep MCMC is $π$-invariant, irreducible, and aperiodic, and obtain bounds on expected energy jump distance and cost per iteration. Empirical results examine the robustness and efficacy of our proposed step size selection procedure, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.
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