Compressed Monte Carlo with application in particle filtering

作     者：Martino, Luca Elvira, Victor 

作者机构：Univ Rey Juan Carlos URJC Dept Signal Proc Mostoles Spain Univ Carlos III Madrid UC3M Getafe Spain Univ Edinburgh Ctr Stat Edinburgh Midlothian Scotland 

出 版 物：《INFORMATION SCIENCES》 (信息科学)

年 卷 期：2021年第553卷

页      面：331-352页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Bayesian inference MCMC importance sampling Particle filtering Gaussian quadrature Sigma points Herding algorithms Distributed algorithms 

摘      要：Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior distributions. For this purpose, Monte Carlo (MC) methods, such as Markov Chain Monte Carlo and importance sampling algorithms, are often employed. In this work, we introduce the theory and practice of a Compressed MC (C-MC) scheme to compress the statistical information contained in a set of random samples. In its basic version, C-MC is strictly related to the stratification technique, a well-known method used for variance reduction purposes. Deterministic C-MC schemes are also presented, which provide very good performance. The compression problem is strictly related to the moment matching approach applied in different filtering techniques, usually called as Gaussian quadrature rules or sigma-point methods. C-MC can be employed in a distributed Bayesian inference framework when cheap and fast communications with a central processor are required. Furthermore, C-MC is useful within particle filtering and adaptive IS algorithms, as shown by three novel schemes introduced in this work. Six numerical results confirm the benefits of the introduced schemes, outperforming the corresponding benchmark methods. A related code is also provided. (C) 2020 Elsevier Inc. All rights reserved.