Del Moral, Pierre; Hu, Peng; Wu, Liming On the concentration properties of interacting particle processes. (English) Zbl 1280.60057 Found. Trends Mach. Learn. 3, No. 3-4, 225-389 (2010). 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. Reviewer: Mihai Gradinaru (Rennes) Cited in 5 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 65C35 Stochastic particle methods 47D08 Schrödinger and Feynman-Kac semigroups 82C22 Interacting particle systems in time-dependent statistical mechanics 65C05 Monte Carlo methods 62G20 Asymptotic properties of nonparametric inference 60E15 Inequalities; stochastic orderings Keywords:Feynman-Kac particle processes; concentration inequalities; advanced Monte Carlo methods; Bayesian statistics; computational physics and biology; stochastic optimization PDFBibTeX XMLCite \textit{P. Del Moral} et al., Found. Trends Mach. Learn. 3, No. 3--4, 225--389 (2010; Zbl 1280.60057) Full Text: DOI arXiv