Foundations and Trends® in Machine Learning > Vol 3 > Issue 3–4

On the Concentration Properties of Interacting Particle Processes

Pierre Del Moral, INRIA, Bordeaux-Sud Ouest Center, INRIA, Bordeaux-Sud Ouest Center & Bordeaux Mathematical Institute, France, pierre.del-moral@inria.fr Peng Hu, INRIA, Bordeaux-Sud Ouest Center, INRIA, Bordeaux-Sud Ouest Center & Bordeaux Mathematical Institute, France, peng.hu@inria.fr Liming Wu, Academy of Mathematics and Systems Science & Laboratoire de Mathématiques, Université Blaise Pascal, France, wuliming@amt.ac.cn
 
Suggested Citation
Pierre Del Moral, Peng Hu and Liming Wu (2012), "On the Concentration Properties of Interacting Particle Processes", Foundations and Trends® in Machine Learning: Vol. 3: No. 3–4, pp 225-389. http://dx.doi.org/10.1561/2200000026

Published: 26 Jan 2012
© 2012 P. Del Moral, P. Hu, and L. Wu
 
Subjects
Bayesian learning,  Markov chain Monte Carlo
 

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In this article:
1 Stochastic Particle Methods
2 Some Application Domains
3 Feynman-Kac Semigroup Analysis
4 Empirical Processes
5 Interacting Empirical Processes
6 Feynman-Kac Particle Processes
References

Abstract

This monograph presents some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution models, particle free energies, as well as backward Markov chain particle models. We illustrate these results with a series of topics related to computational physics and biology, stochastic optimization, signal processing and Bayesian statistics, and many other probabilistic machine learning algorithms. Special emphasis is given to the stochastic modeling, and to the quantitative performance analysis of a series of advanced Monte Carlo methods, including particle filters, genetic type island models, Markov bridge models, and interacting particle Markov chain Monte Carlo methodologies.

DOI:10.1561/2200000026
ISBN: 978-1-60198-512-5
176 pp. $99.00
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ISBN: 978-1-60198-513-2
176 pp. $200.00
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Table of contents:
1: Stochastic particle methods
2: Some application domains
3: Feynman-Kac semigroup analysis
4: Empirical processes
5: Interacting empirical processes
6: Feynman-Kac particle processes
References

On the Concentration Properties of Interacting Particle Processes

This book presents some new concentration inequalities for Feynman-Kac particle processes. It analyzes different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution models, particle free energies, as well as backward Markov chain particle models. It illustrates these results with a series of topics related to computational physics and biology, stochastic optimization, signal processing and Bayesian statistics, and many other probabilistic machine learning algorithms. Special emphasis is given to the stochastic modeling, and to the quantitative performance analysis of a series of advanced Monte Carlo methods; including particle filters, genetic type island models, Markov bridge models, and interacting particle Markov chain Monte Carlo methodologies.

 
MAL-026