The average sensitivity of an intersection of half spaces

• Published in: Research in the mathematical sciences Vol. 1; no. 1
• Main Author: Kane, Daniel
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2014
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematics; Mathematics and Statistics; Boolean function; Noise sensitivity; Halfspaces; Machine learning

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 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,...