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

Shaojie Li; Yong Liu

ICML 2023poster1 citations

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

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.

BibTeX

@inproceedings{icml2023_distributiondepe,
  title = {Distribution-dependent McDiarmid-type Inequalities for Functions of Unbounded Interaction},
  author = {Shaojie Li and Yong Liu},
  booktitle = {ICML 2023},
  year = {2023}
}