Optimal Approximations Made Easy
This work simplifies a foundational tool used in learning theory, algorithms, and other fields, making it easier to teach and understand, but it is incremental as it does not introduce new results.
The paper provides a modular, self-contained proof of the Li, Long, and Srinivasan result on approximations of set systems for finite cases, using only Chernoff's bound to make it accessible for teaching and broader audiences.
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.