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

Shaojie Li, Yong Liu
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:19789-19810, 2023.

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 this Paper

BibTeX
@InProceedings{pmlr-v202-li23t, title = {Distribution-dependent {M}c{D}iarmid-type Inequalities for Functions of Unbounded Interaction}, author = {Li, Shaojie and Liu, Yong}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {19789--19810}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/li23t/li23t.pdf}, url = {https://proceedings.mlr.press/v202/li23t.html}, 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.} }
Endnote
%0 Conference Paper %T Distribution-dependent McDiarmid-type Inequalities for Functions of Unbounded Interaction %A Shaojie Li %A Yong Liu %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-li23t %I PMLR %P 19789--19810 %U https://proceedings.mlr.press/v202/li23t.html %V 202 %X 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.
APA
Li, S. & Liu, Y.. (2023). Distribution-dependent McDiarmid-type Inequalities for Functions of Unbounded Interaction. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:19789-19810 Available from https://proceedings.mlr.press/v202/li23t.html.

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