A FRAMEWORK FOR ADAPTIVE MCMC TARGETING MULTIMODAL DISTRIBUTIONS

• 成果类型: Article
• 署名作者: Pompe, Emilia; Holmes, Chris; Latuszynski, Krzysztof
• 署名单位: University of Oxford; University of Warwick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1916
• 发表日期: 2020
• 页码: 2930-2952
• 关键词: chain; ergodicity; CONVERGENCE; inference; efficient; parallel; algorithm

摘要

We propose a new Monte Carlo method for sampling from multimodal distributions. The idea of this technique is based on splitting the task into two: finding the modes of a target distribution pi and sampling, given the knowledge of the locations of the modes. The sampling algorithm relies on steps of two types: local ones, preserving the mode; and jumps to regions associated with different modes. Besides, the method learns the optimal parameters of the algorithm, while it runs, without requiring user intervention. Our technique should be considered as a flexible framework, in which the design of moves can follow various strategies known from the broad MCMC literature. In order to design an adaptive scheme that facilitates both local and jump moves, we introduce an auxiliary variable representing each mode, and we define a new target distribution (pi) over tilde on an augmented state space X x I, where X is the original state space of pi and I is the set of the modes. As the algorithm runs and updates its parameters, the target distribution (pi) over tilde also keeps being modified. This motivates a new class of algorithms, Auxiliary Variable Adaptive MCMC. We prove general ergodic results for the whole class before specialising to the case of our algorithm.