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Poster
Chebyshev-Cantelli PAC-Bayes-Bennett Inequality for the Weighted Majority Vote
Yi-Shan Wu · Andres Masegosa · Stephan Lorenzen · Christian Igel · Yevgeny Seldin

Thu Dec 09 12:30 AM -- 02:00 AM (PST) @
in Poster Session 5 »

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.

Keywords: Theory · Optimization

Author Information

Yi-Shan Wu (University of Copenhagen)
Andres Masegosa (Aalborg University)
Stephan Lorenzen (University of Copenhagen)
Christian Igel (University of Copenhagen)
Yevgeny Seldin (University of Copenhagen)

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