Compressed Monte Carlo with application in particle filtering

TL;DR

This paper introduces Compressed Monte Carlo (C-MC), a method to efficiently compress and utilize samples in Bayesian inference, particle filtering, and importance sampling, demonstrating improved performance over existing techniques.

Contribution

The paper develops the theory and practical schemes of C-MC, including deterministic variants, for efficient sample compression in Bayesian inference and filtering applications.

Findings

C-MC outperforms benchmark methods in numerical tests.

Deterministic C-MC schemes show very good performance.

C-MC is effective in distributed Bayesian inference and particle filtering.

Abstract

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.