The average sensitivity of an intersection of half spaces

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,...

Full description

Saved in:
Bibliographic Details
Published inResearch in the mathematical sciences Vol. 1; no. 1
Main Author Kane, Daniel
Format Journal Article
LanguageEnglish
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
Online AccessGet full text

Cover

More Information
Summary: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, Klivans and Meka. Furthermore, our result has implications for the runtime required to learn intersections of halfspaces. AMS Subject Classification Primary; 52C45
ISSN:2197-9847
2197-9847
DOI:10.1186/s40687-014-0013-6