Chebyshev-Cantelli PAC-Bayes-Bennett Inequality for the Weighted Majority Vote
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
We present a new second-order oracle bound for the expected risk of a weighted majority vote. The bound is based on a novel parametric form of the Chebyshev-Cantelli inequality (a.k.a. one-sided Chebyshev’s), which is amenable to efficient minimization. The new form resolves the optimization challenge faced by prior oracle bounds based on the Chebyshev-Cantelli inequality, the C-bounds [Germain et al., 2015], and, at the same time, it improves on the oracle bound based on second order Markov’s inequality introduced by Masegosa et al. [2020]. We also derive a new concentration of measure inequality, which we name PAC-Bayes-Bennett, since it combines PAC-Bayesian bounding with Bennett’s inequality. We use it for empirical estimation of the oracle bound. The PAC-Bayes-Bennett inequality improves on the PAC-Bayes-Bernstein inequality of Seldin et al. [2012]. We provide an empirical evaluation demonstrating that the new bounds can improve on the work of Masegosa et al. [2020]. Both the parametric form of the Chebyshev-Cantelli inequality and the PAC-Bayes-Bennett inequality may be of independent interest for the study of concentration of measure in other domains.
Original language | English |
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Title of host publication | Advances in Neural Information Processing Systems 34 (NeurIPS) |
Publisher | NeurIPS Proceedings |
Publication date | 2021 |
Pages | 1-12 |
Publication status | Published - 2021 |
Event | 35th Conference on Neural Information Processing Systems (NeurIPS 2021) - Virtuel Duration: 6 Dec 2021 → 14 Dec 2021 |
Conference
Conference | 35th Conference on Neural Information Processing Systems (NeurIPS 2021) |
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By | Virtuel |
Periode | 06/12/2021 → 14/12/2021 |
Links
- https://proceedings.neurips.cc/paper/2021/file/69386f6bb1dfed68692a24c8686939b9-Paper.pdf
Final published version
ID: 298390373