Corpus ID: 12792949

# Nearly Tight Bounds on ℓ1 Approximation of Self-Bounding Functions

@article{Feldman2014NearlyTB,
title={Nearly Tight Bounds on ℓ1 Approximation of Self-Bounding Functions},
author={V. Feldman and Pravesh Kothari and J. Vondr{\'a}k},
journal={ArXiv},
year={2014},
volume={abs/1404.4702}
}
• Published 2014
• Mathematics, Computer Science
• ArXiv
• We study the complexity of learning and approximation of self-bounding functions over the uniform distribution on the Boolean hypercube ${0,1}^n$. Informally, a function $f:{0,1}^n \rightarrow \mathbb{R}$ is self-bounding if for every $x \in {0,1}^n$, $f(x)$ upper bounds the sum of all the $n$ marginal decreases in the value of the function at $x$. Self-bounding functions include such well-known classes of functions as submodular and fractionally-subadditive (XOS) functions. They were… CONTINUE READING
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