Distribution-dependent McDiarmid-type Inequalities for Functions of Unbounded Interaction

Published: 24 Apr 2023, Last Modified: 21 Jun 2023ICML 2023 PosterEveryoneRevisions
Abstract: The concentration of measure inequalities serves an essential role in statistics and machine learning. This paper gives unbounded analogues of the McDiarmid-type exponential inequalities for three popular classes of distributions, namely sub-Gaussian, sub-exponential and heavy-tailed distributions. The inequalities in the sub-Gaussian and sub-exponential cases are distribution-dependent compared with the recent results, and the inequalities in the heavy-tailed case are not available in the previous works. The usefulness of the inequalities is illustrated through applications to the sample mean, U-statistics and V-statistics.
Submission Number: 2639