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/}
}