Concentration Inequalities Under Sub-Gaussian and Sub-Exponential Conditions

Abstract

We prove analogues of the popular bounded difference inequality (also called McDiarmid's inequality) for functions of independent random variables under sub-gaussian and sub-exponential conditions. Applied to vector-valued concentration and the method of Rademacher complexities these inequalities allow an easy extension of uniform convergence results for PCA and linear regression to the case potentially unbounded input- and output variables.

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Cite

Text

Maurer and Pontil. "Concentration Inequalities Under Sub-Gaussian and Sub-Exponential Conditions." Neural Information Processing Systems, 2021.

Markdown

[Maurer and Pontil. "Concentration Inequalities Under Sub-Gaussian and Sub-Exponential Conditions." Neural Information Processing Systems, 2021.](https://mlanthology.org/neurips/2021/maurer2021neurips-concentration/)

BibTeX

@inproceedings{maurer2021neurips-concentration,
  title     = {{Concentration Inequalities Under Sub-Gaussian and Sub-Exponential Conditions}},
  author    = {Maurer, Andreas and Pontil, Massimiliano},
  booktitle = {Neural Information Processing Systems},
  year      = {2021},
  url       = {https://mlanthology.org/neurips/2021/maurer2021neurips-concentration/}
}