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We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of non-contracting chains.
Extension of the law of large numbers to dependent quantities
Andrei A. Markov · 1906
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Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator
Aryeh Dvoretzky, Jack Kiefer, and Jacob Wolfowitz · 1956
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The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality
Pascal Massart · 1990
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Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process
James Allen Fill · 1991
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A probability inequality for the occupation measure of a reversible Markov chain
Ian H. Dinwoodie · 1995
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Logarithmic Sobolev inequalities for finite Markov chains
Persi Diaconis and Laurent Saloff-Coste · 1996
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Nash inequalities for finite Markov chains
Persi Diaconis and Laurent Saloff-Coste · 1996
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Bounding d ¯ \bar{d} -distance by informational divergence: a method to prove measure concentration
Katalin Marton · 1996
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Large deviation bounds for Markov chains
Nabil Kahale · 1997
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Expectations for nonreversible Markov chains
Ian H. Dinwoodie · 1998
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A Chernoff bound for random walks on expander graphs
David Gillman · 1998
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Chernoff-type bound for finite Markov chains
Pascal Lezaud · 1998
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Measure concentration for a class of random processes
Katalin Marton · 1998
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Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues
Pierre Brémaud · 1999
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Inégalités de Hoeffding pour les fonctions lipschitziennes de suites dépendantes
Emmanuel Rio · 2000
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Concentration of measure inequalities for Markov chains and Φ \Phi -mixing processes
Paul-Marie Samson · 2000
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Measure concentration and strong mixing
Katalin Marton · 2003
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Optimal Hoeffding bounds for discrete reversible Markov chains
Carlos A. León and François Perron · 2004
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Concentration inequalities for Markov processes via coupling
Jean-René Chazottes and Frank Redig · 2009
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A spectral algorithm for learning hidden Markov models
Daniel Hsu, Sham M. Kakade, and Tong Zhang · 2009
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Concentration of empirical distribution functions with applications to non-i.i.d. models
S. G. Bobkov and F. Götze · 2010
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Reduced-rank Hidden Markov Models
Sajid M. Siddiqi, Byron Boots, and Geoffrey J. Gordon · 2010
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Exponential concentration inequalities for additive functionals of Markov chains (arxiv:1201.3569v1)
Radosław Adamczak and Witold Bednorz · 2012
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A method of moments for mixture models and hidden Markov models
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Measure concentration for Euclidean distance in the case of dependent random variables
Katalin Marton · 2004
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Learning nonsingular phylogenies and hidden Markov models
Elchanan Mossel and Sébastien Roch · 2006
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Concentration inequalities for random fields via coupling
Jean-René Chazottes, Pierre Collet, Christof Külske, and Frank Redig · 2007
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A tail inequality for suprema of unbounded empirical processes with applications to Markov chains
Radosław Adamczak · 2008
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Concentration Inequalities for Dependent Random Variables via the Martingale Method
Leonid (Aryeh) Kontorovich and Kavita Ramanan · 2008
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Tail estimates for sums of variables sampled by a random walk
Roy Wagner · 2008
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Animashree Anandkumar, Daniel Hsu, and Sham M. Kakade · 2012
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Chernoff-hoeffding bounds for Markov chains: Generalized and simplified
Kai-Min Chung, Henry Lam, Zhenming Liu, and Michael Mitzenmacher · 2012
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Obtaining measure concentration from Markov contraction
Aryeh Kontorovich · 2012
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Geometric ergodicity and the spectral gap of non-reversible Markov chains
I. Kontoyiannis and S.P. Meyn · 2012
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A sharp estimate of the binomial mean absolute deviation with applications
Daniel Berend and Aryeh Kontorovich · 2013
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Aryeh Kontorovich, Boaz Nadler, and Roi Weiss · 2013
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Contrastive learning using spectral methods
David C. Parkes, Ryan P. Adams, Daniel Hsu, and James Y. Zou · 2013
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