Measure Concentration of Markov Tree Processes

2006/08/21 by Leonid Kontorovich, Kontorovich, Leonid · 2 citations
Computer Science · Mathematics · #60G07 #Bayesian Methods and Mixture Models #FOS: Mathematics #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #math.FA #math.PR #msc:60G07

paper · pdf · doi:10.48550/arxiv.math/0608511

14 pages

openalex publication_date 2006/08/21 · arxiv created 2006/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an apparently novel concentration of measure result for Markov tree processes. The bound we derive reduces to the known bounds for Markov processes when the tree is a chain, thus strictly generalizing the known Markov process concentration results. We employ several techniques of potential independent interest, especially for obtaining similar results for more general directed acyclic graphical models.

Cited by

• Obtaining Measure Concentration from Markov Contraction
• Metric and Mixing Sufficient Conditions for Concentration of Measure

Related

• Measure Concentration of Hidden Markov Processes
• Obtaining Measure Concentration from Markov Contraction
• Concentration of measure and mixing for Markov chains
• Uniform Chernoff and Dvoretzky-Kiefer-Wolfowitz-type inequalities for Markov chains and related processes
• Concentration and mean field approximation results for Markov processes on large networks