The Average Sensitivity of an Intersection of Half Spaces

Daniel M. Kane

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arXiv · 1309.2987

The Average Sensitivity of an Intersection of Half Spaces

Daniel M. Kane

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Abstract

We prove new bounds on the average sensitivity of the indicator function of an intersection of $k$ halfspaces. In particular, we prove the optimal bound of $O(\sqrt{n\log(k)})$. This generalizes a result of Nazarov, who proved the analogous result in the Gaussian case, and improves upon a result of Harsha, Klivans and Meka. Furthermore, our result has implications for the runtime required to learn intersections of halfspaces.

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Daniel M. Kane. 2013-09-11. The Average Sensitivity of an Intersection of Half Spaces. https://arxiv.org/abs/1309.2987

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