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arXiv 2008.08970cs.LGcs.CGmath.COstat.ML

Optimal Approximations Made Easy

Université Gustave Eiffel(古斯塔夫·埃菲尔大学);ESIEE Paris(巴黎高等电子与电工技术工程师学院);Université Sorbonne Paris Nord(巴黎索邦北大学);CNRS(法国国家科学研究中心)

Mónika Csikós, Nabil H. Mustafa

英文摘要:

The fundamental result of Li, Long, and Srinivasan on approximations of set systems has become a key tool across several communities such as learning theory, algorithms, computational geometry, combinatorics and data analysis. The goal of this paper is to give a modular, self-contained, intuitive proof of this result for finite set systems. The only ingredient we assume is the standard Chernoff's concentration bound. This makes the proof accessible to a wider audience, readers not familiar with techniques from statistical learning theory, and makes it possible to be covered in a single self-contained lecture in a geometry, algorithms or combinatorics course.

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