Concentration Inequalities With Exchangeable Pairs

By Sourav Chatterjee. 2005

103 citations recorded by the source corpus.

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Citations in the corpus

A short survey of Stein's method (2014, background): “One of the main results of [18, 20] is that if (W,W ) is an exchangeable pair of random variables and F (W,W ) is an antisymmetric function of (W,W ) (meaning that F (W,W ) = −F (W ,W )), then for all t ≥ 0, P(|f(W )| ≥ t) ≤ 2e−t2/2C , where f(W ) = E(F (W,W ′)|W ) and C is a number such that |(f(W ”
An Introduction to Matrix Concentration Inequalities (2015, unknown): “This approach extends a scalar argument, introduced by Chatterjee [38, 39], that depends on exchangeable pairs and Markov chain couplings.”
Hash Kernels (2009, background): “Bounds for exchangeable random variables, in particular [Chatterjee, 2005, Theorem 3.3], can be used to obtain an exponential inequality in of the form required by Theorem 2, albeit without providing the desired dependency on n.”
A NEW METHOD OF NORMAL APPROXIMATION (2006, methodology): “It is closely connected to certain techniques introduced in the author’s previous works [8, 9].”
Stein couplings for normal approximation (2010, methodology): “In Chatterjee (2007) this construction is used to prove concentration of measure results for such W .”
Applications of Stein's method for concentration inequalities (2009, background): “A selection of results and examples from [10] appeared in the later papers [11, 12].”
Concentration Inequalities for Dependent Random Variables via the Martingale Method (2006, background): “…phenomenon has been quite extensively studied in the case when P is a product measure on a product space ( ,F ) or, equivalently, when ϕ is a function of a large number of i.i.d. random variables (see, e.g., the surveys of Talagrand [29, 30], Ledoux [17], McDiarmid [25] and references therein).”
An introduction to large deviations for random graphs (2016, background): “rem 5.6 gives a nonlinear example. Theorems 7.1 and 7.2 are consequences of this approximation where φp(t) is explicitly computable in a limit. The main result of [17], building on ideas developed in [14, 15, 18], gives a suﬃcient condition under which (8.2) is valid for a general nonlinear f. The c”