# Approximate resilience, monotonicity, and the complexity of agnostic learning

@inproceedings{DachmanSoled2015ApproximateRM, title={Approximate resilience, monotonicity, and the complexity of agnostic learning}, author={Dana Dachman-Soled and Vitaly Feldman and Li-Yang Tan and Andrew Wan and Karl Wimmer}, booktitle={SODA}, year={2015} }

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 $\mathit{approximate}$ $\mathit{resilience}$ of Boolean functions, where we say that $f$ is $\alpha$-approximately $d$-resilient if $f$ is $\alpha$-close to a $[-1,1]$-valued $d$-resilient function in $\ell_1$ distance. We show that approximate resilience essentially characterizes the complexity of agnostic learning of a… CONTINUE READING

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