Concentration inequalities for the exponential weighting method

Stein’s Method for Concentration Inequalities

We introduce a version of Stein’s method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.

Aggregation by Exponential Weighting and Sharp Oracle Inequalities

Applications of Stein’s Method for Concentration Inequalities

Stein’s method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the theory and three applications: (1) We obtain a concentration inequality for the magnetization in the Curie-Weiss model at critical temperature (where it obeys a n...

Concentration inequalities using the entropy method

We investigate a new methodology, worked out by Ledoux and Mas-sart, to prove concentration-of-measure inequalities. The method is based on certain modified logarithmic Sobolev inequalities. We provide some very simple and general ready-to-use inequalities. One of these inequalities may be considered as an exponential version of the Efron-Stein inequality. The main purpose of this paper is to p...

Concentration Inequalities for Dependent Random Variables via the Martingale Method

Abstract: We use the martingale method to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, we obtain bounds on certain martingale differences associated with the random sequences, which may be of independent interest. As an applicatio...