# Compressed Monte Carlo with application in particle filtering

arXiv: https://arxiv.org/abs/2107.08459 · HTML: https://mlsanity.com/paper/2107.08459/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 53 references that are in the map.
- First posted on arXiv 18 Jul 2021.

## Builds on (most cited first, 7 of 7)

- [Stein Points](https://mlsanity.com/paper/1803.10161/) (2018)
- [Support points](https://mlsanity.com/paper/1609.01811/) (2016)
- [Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering](https://mlsanity.com/paper/1501.02056/) (2015)
- [Layered Adaptive Importance Sampling](https://mlsanity.com/paper/1505.04732/) (2015)
- [Markov Chain Importance Sampling -- a highly efficient estimator for MCMC](https://mlsanity.com/paper/1805.07179/) (2018)
- [Group Importance Sampling for Particle Filtering and MCMC](https://mlsanity.com/paper/1704.02771/) (2017)
- [Projected support points: a new method for high-dimensional data reduction](https://mlsanity.com/paper/1708.06897/) (2017)

## Built on by (most cited first, 3 of 3)

- [In Defense and Revival of Bayesian Filtering for Thermal Infrared Object Tracking](https://mlsanity.com/paper/2402.17098/) (2024)
- [Spectral information criterion for automatic elbow detection](https://mlsanity.com/paper/2308.09108/) (2023)
- [Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals](https://mlsanity.com/paper/2501.01148/) (2025)

## Abstract (arXiv)

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.