CONCENTRATION OF MEASURE INEQUALITIES FOR MARKOV CHAINS AND -MIXING PROCESSES By Paul-Marie Samson

2000

Citations in the corpus

• Bernstein's inequalities for general Markov chains (2018, unknown): “…research includes Marton’s work on the concentration of measure phenomenon for contracting Markov chains (Marton, 1996a,b, 1998, 2003, 2004) and further progresses under various dependence structures (Samson, 2000; Chazottes et al., 2007; Kontorovich and Ramanan, 2008; Redig and Chazottes, 2009).”
• Transport Inequalities. A Survey (2010, background): “Other forms of non-product tensorizations have been studied (see [77, 78, 79, 80], [94] or [37, 112]) in the context of Markov chains or Gibbs measures (see Section 11).”
• On a mixture of Brenier and Strassen Theorems (2018, methodology): “These barycentric costs are actually part of a more general family of transport costs, called “weak transport costs” or “generalized transport costs”, introduced under the first name by the first author together with Roberto, Samson and Tetali in [33] (see Section 1.4 below for a more complete present”
• Learning from Limited Demonstrations (2013, methodology): “For example, the i.i.d. assumption A1 can be relaxed using independent block technique [18] or other techniques to handle dependent data, e.g., [19].”
• Chernoff and Berry-Esséen inequalities for Markov processes (2001, methodology): “Finally, an approach based on the concentration inequalities developped by [22] and [24] gives deviation inequalities for Markov chains.”
• Learning Kernels with Random Features (2016, methodology): “Using Samson’s sub-Gaussian concentration inequality [26] for Lipschitz convex functions of bounded random variables, we have with probability at least least 1− δ that”
• User-friendly introduction to PAC-Bayes bounds (2021, background): “Li [6] for (less general) mixing time series thanks to Samson’s version of Bernstein’s inequality [172].”
• Regularized Policy Iteration with Nonparametric Function Spaces (2016, methodology): “For these processes, tools such as the independent blocks technique (Yu, 1994; Doukhan, 1994) or information theoretical inequalities (Samson, 2000) can be used to carry on the analysis—as have been done by Antos et al.”
• Stability Bounds for Stationary φ-mixing and β-mixing Processes (2008, background): “Several concentration inequalities have been shown in ϕ -mixing case, e.g. Marton (1998); Samson (2000); Chazottes et al. (2007); Kontorovich and Ramanan (2006).”
• Subgaussian concentration inequalities for geometrically ergodic Markov chains (2014, unknown): “2) and [16] for other concentration inequalities).”
• Displacement convexity of entropy and related inequalities on graphs (2012, background): “For more on this Wasserstein-type distance, see [11,35,51].”
• Regularization in reinforcement learning (2011, methodology): “The following proposition, extracted from the discussion on pages 421–422 of the paper by Samson [2000], gives such a condition.”
• A tail inequality for suprema of unbounded empirical processes with applications to Markov chains (2007, methodology): “Additionally, in Samson’s estimate there is no log n factor, which is present in Theorems 6 and 7.”
• Concentration Inequalities (2008, methodology): “Originally, martingale methods dominated the research (see, e.g., McDiarmid [2] [3], Rhee and Talagrand [59], Shamir and Spencer [60]) but independently information-theoretic methods were also used with success (see Alhswede, Gács, and Körner [4], Marton [5] [6] [7], Dembo [8], Massart [9], Rio [10]”