Abstract
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.
Originalsprog | Engelsk |
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Titel | Advances in Neural Information Processing Systems (NeurIPS 2021) |
Antal sider | 12 |
Vol/bind | 34 |
Publikationsdato | 2021 |
Status | Udgivet - 2021 |
Begivenhed | Thirty-fifth Conference on Neural Information Processing Systems -NeurIPS 2021 - Virtual-only Conference Varighed: 6 dec. 2021 → 14 dec. 2021 |
Konference
Konference | Thirty-fifth Conference on Neural Information Processing Systems -NeurIPS 2021 |
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Lokation | Virtual-only Conference |
Periode | 06/12/2021 → 14/12/2021 |