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DM Kane (2010)
Proceedings of the 25th Annual Conference on Computational Complexity
AT Kalai, AR Klivans, Y Mansour, RA Servedio (2005)
Proceedings of the 46th Foundations of Computer Science
C Gotsman, N Linial (1994)
Spectral properties of threshold functionsCombinatorica, 14
P Harsha, AR Kilvans, R Meka (2010)
Proceedings of the 42nd ACM Symposium on Theory of Computing
Department of Computer Science and Engineering, 9500 Gilman Drive We prove new bounds on the average sensitivity of the indicator function of an #0404, La Jolla, CA 92093-0404, USA intersection of k halfspaces. In particular, we prove the optimal bound of O 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. AMS Subject Classification: Primary; 52C45 Keywords: Boolean function; Halfspaces; Noise sensitivity; Machine learning Background One of the most important measures of the complexity of a Boolean function f : R → {±1} is that of its average sensitivity, namely AS( f ) : = E #{i : f (x) = f (x )} x∼ {±1} i th where x above is x with the i coordinate flipped. The average sensitivity and related measures of noise sensitivity of a Boolean function have found several applications, per- haps most notably to the area of machine learning (see for example [1]). It has thus become important to understand how large the average sensitivity of functions in various classes
Research in the Mathematical Sciences – Springer Journals
Published: Nov 11, 2014
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