Approximate resilience, monotonicity, and the complexity of agnostic learning

Abstract

A function f is d-resilient if all its Fourier coefficients of degree at most d are zero, i.e. f is uncorrelated with all low-degree parities. We study the notion of approximate resilience of Boolean functions, where we say that f is α-approximately d-resilient if f is α-close to a [−1, 1]-valued d-resilient function in `1 distance. We show that approximate… (More)
DOI: 10.1137/1.9781611973730.34

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