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.
Original language | English |
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Title of host publication | Advances in Neural Information Processing Systems (NeurIPS 2021) |
Number of pages | 12 |
Volume | 34 |
Publication date | 2021 |
Publication status | Published - 2021 |
Event | Thirty-fifth Conference on Neural Information Processing Systems -NeurIPS 2021 - Virtual-only Conference Duration: 6 Dec 2021 → 14 Dec 2021 |
Conference
Conference | Thirty-fifth Conference on Neural Information Processing Systems -NeurIPS 2021 |
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Location | Virtual-only Conference |
Period | 06/12/2021 → 14/12/2021 |
Bibliographical note
BFI Level 2Keywords
- Machine Learning
- Ensemble Methods
- Majority Vote
- PAC-Bayesian