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.
Cite
Text
Li and Liu. "Distribution-Dependent McDiarmid-Type Inequalities for Functions of Unbounded Interaction." International Conference on Machine Learning, 2023.Markdown
[Li and Liu. "Distribution-Dependent McDiarmid-Type Inequalities for Functions of Unbounded Interaction." International Conference on Machine Learning, 2023.](https://mlanthology.org/icml/2023/li2023icml-distributiondependent/)BibTeX
@inproceedings{li2023icml-distributiondependent,
title = {{Distribution-Dependent McDiarmid-Type Inequalities for Functions of Unbounded Interaction}},
author = {Li, Shaojie and Liu, Yong},
booktitle = {International Conference on Machine Learning},
year = {2023},
pages = {19789-19810},
volume = {202},
url = {https://mlanthology.org/icml/2023/li2023icml-distributiondependent/}
}