Concentration of measure inequalities for Markov chains and $\Phi$-mixing processes

By Paul-Marie Samson. 2000

208 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

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Citations in the corpus

Variance-based Regularization with Convex Objectives (2016, methodology): “ummarizing, we ﬁnd that P N1 > n 2 or N−1 > n 2 ≥ 2Φ − r nδ2 1 −δ2 ! −(1 −δ2)n/2 r 8 πn . 39 A.2 Proof of Lemma 6.3 We use two technical lemmas in the proof of this lemma. Lemma A.1 (Samson [31], Corollary 3). Let f : Rn → R be convex and L-Lipschitz continuous with respect to the ℓ2-norm ov”
Transport Inequalities. A Survey (2010, background): “Other forms of non-product tensorizations have been studied (see [77–80,94] or [37,112]) in the context of Markov chains or Gibbs measures (see Section 11).”
On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries (2011, unknown): “[22, 32]).”
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.”
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.”
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.”
A note on the Hanson-Wright inequality for random vectors with dependencies (2014, methodology): “• An extension of Talagrand’s result has been provided by Samson [27] and Paulin [24], who obtained concentration for vectors with bounded coordinates, satisfying some uniform mixing conditions or Dobrushin type criteria.”
Learning from Limited Demonstrations (2013, unknown): “, [19].”
Concentration inequalities for Markov chains by Marton couplings and spectral methods (2012, methodology): “Finally, [35] further develops the results of [45], and introduces the coupling structure that we call Marton coupling in this paper.”
Kantorovich duality for general transport costs and applications (2014, methodology): “N. Gozlan, C. Roberto, and P.-M. Samson, From concentration to logarithmic Sobolev and Poincaré inequalities, J. Funct.”
Displacement convexity of entropy and related inequalities on graphs (2012, background): “For more on this Wasserstein-type distance, see [11, 33, 49] .”