论文标题

大都市调整后的兰格文轨迹的自适应调整

Adaptive Tuning for Metropolis Adjusted Langevin Trajectories

论文作者

Riou-Durand, Lionel, Sountsov, Pavel, Vogrinc, Jure, Margossian, Charles C., Power, Sam

论文摘要

哈密​​顿蒙特卡洛(HMC)是一种用于连续概率分布的广泛使用的采样器。在许多情况下,基本的哈密顿动力学表现出共鸣的现象,可降低算法的效率,使其对高参数值非常敏感。可以通过使用轨迹长度随机化(RHMC)或通过部分动量茶点来有效解决此问题。第二种方法与动力学Langevin扩散有关,并且主要通过使用广义HMC(GHMC)进行了研究。但是,GHMC诱导动量反转,导致采样器回溯和浪费计算资源。在这项工作中,我们着重于最近绕过此问题的算法,名为Metropolis调整后的Langevin轨迹(MALT)。我们基于调整RHMC的超参数的最新策略,该策略针对有效的样本量(ESS)并将其适应麦芽,从而使该算法的第一个用户友好地部署。我们构建了一种方法,以优化ESS上的更清晰的绑定并减少估计器差异。与GHMC,RHMC和NUTS相比,在ESS速率方面很容易与并行实施兼容,在ESS速率方面具有竞争力,并且在记忆使用方面具有有用的权衡。

Hamiltonian Monte Carlo (HMC) is a widely used sampler for continuous probability distributions. In many cases, the underlying Hamiltonian dynamics exhibit a phenomenon of resonance which decreases the efficiency of the algorithm and makes it very sensitive to hyperparameter values. This issue can be tackled efficiently, either via the use of trajectory length randomization (RHMC) or via partial momentum refreshment. The second approach is connected to the kinetic Langevin diffusion, and has been mostly investigated through the use of Generalized HMC (GHMC). However, GHMC induces momentum flips upon rejections causing the sampler to backtrack and waste computational resources. In this work we focus on a recent algorithm bypassing this issue, named Metropolis Adjusted Langevin Trajectories (MALT). We build upon recent strategies for tuning the hyperparameters of RHMC which target a bound on the Effective Sample Size (ESS) and adapt it to MALT, thereby enabling the first user-friendly deployment of this algorithm. We construct a method to optimize a sharper bound on the ESS and reduce the estimator variance. Easily compatible with parallel implementation, the resultant Adaptive MALT algorithm is competitive in terms of ESS rate and hits useful tradeoffs in memory usage when compared to GHMC, RHMC and NUTS.

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源