Optimal approximations made easy

•We consider the fundamental result of Li, Long, and Srinivasan on optimal approximations for finite set systems.•We give a modular, intuitive proof of their result for finite set systems. The only tool we assume is Chernoff's bound.•This new proof can be covered in a single self-contained lect...

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Bibliographic Details
Published in:Information processing letters 2022-06, Vol.176, p.106250, Article 106250
Main Authors: Csikós, Mónika, Mustafa, Nabil H.
Format: Article
Language:English
Subjects:
Analysis of algorithms
Chaining
Computer Science
Data Analysis, Statistics and Probability
Physics
Random sampling
Symmetrization
VC theory
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Summary:•We consider the fundamental result of Li, Long, and Srinivasan on optimal approximations for finite set systems.•We give a modular, intuitive proof of their result for finite set systems. The only tool we assume is Chernoff's bound.•This new proof can be covered in a single self-contained lecture in a geometry, algorithms or combinatorics course. The fundamental result of Li, Long, and Srinivasan [14] 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.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2022.106250