通过学习跳跃步长加速哈密顿蒙特卡洛：一种自校准随机化解决方案
Faster Hamiltonian Monte Carlo by Learning Leapfrog Scale: an offline randomized solution
AI总结：
提出一种基于随机选择积分时间的哈密顿蒙特卡洛方法eHMC，通过离线校准阶段利用重要性采样构建离散化参数的经验分布，无需手动退火诊断和在线自适应，在基准测试中与NUTS相比具有竞争或更高的效率。
摘要：
我们介绍了一种基于随机选择积分时间的哈密顿蒙特卡洛（HMC）方法，称为eHMC，其中“e”代表经验。该方法依赖于离线校准阶段，利用重要性采样构建离散化参数的经验分布，从而消除了手动退火诊断和在线自适应的需要。校准阶段中使用的提议分布是通过种群蒙特卡洛方案结合退火和灵活的参数变分族（如归一化流）获得的。所得算法定义了一个具有固定混合分布的HMC核混合，保持了目标分布。在基准测试上的数值实验表明，在考虑计算成本时，eHMC与No-U-Turn采样器（NUTS）相比实现了具有竞争力或更高的效率。这些结果表明，离线校准结合随机化积分方案为自适应HMC方法提供了一种可行的替代方案。
英文摘要：
We introduce a Hamiltonian Monte Carlo (HMC) methodology based on an offline empirical calibration of randomized leapfrog parameters. The approach, referred to as eHMC, where \textit{e} stands for empirical, leverages importance sampling to construct an empirical distribution on discretization parameters, thereby eliminating the need for manual burn-in diagnostics and online adaptation. The proposal distribution used in the calibration stage is obtained via a Population Monte Carlo scheme with tempering and relies on flexible parametric variational families such as normalizing flows. Once the calibration stage complete, the resulting algorithm defines a homogeneous Markov chain via a mixture of HMC kernels with a fixed mixing distribution, and hence preserves the target distribution. Numerical experiments indicate that eHMC can achieve competitive or improved sampling efficiency compared to the No-U-Turn Sampler (NUTS) in the case useful integration times can be summarized by the offline distribution. The comparison is assessed by standard efficiency metrics normalized by the number of leapfrog steps during the post-calibration sampling phase.
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