Abstract
We consider a problem of supervised statistical learning for a finite population and obtain PAC generalization bounds within the combinatorial PAC framework. Combinatorial counterparts of Langford shell bounds are obtained and are shown to be either the particular case of the Occam razor bound or a variant of Vapnik-Chervonenkis bound and similarly loose in both cases. The reasons for looseness of shell bounds are analyzed, the bounds are compared experimentally.
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Denis A. Kochedykov. Graduated from Moscow State University, Computational Mathematics and Cybernatics Department (Master’s degree in Applied Mathematics) in 2005 and from Far Eastern State University (Specialist degree in Theoretical Physics) in 2001. At present, doctoral candidate at Dorodnicyn Computing Centre, Russian Academy of Sciences. Scientific interests: machine learning, statistics, statistical learning theory, and combinatorics.
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Kochedykov, D.A. Combinatorial shell bounds for generalization ability. Pattern Recognit. Image Anal. 20, 459–473 (2010). https://doi.org/10.1134/S1054661810040061
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DOI: https://doi.org/10.1134/S1054661810040061