Learning juntas

Authors:
Elchanan Mossel;Ryan O'Donnell;Rocco P. Servedio
Affiliations:
U.C. Berkeley, Berkeley, CA;MIT, Cambridge, MA;Columbia University, New York, NY
Venue:
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Year:
2003

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Inferring Boolean functions via higher-order correlations

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Abstract

We consider a fundamental problem in computational learning theory: learning an arbitrary Boolean function which depends on an unknown set of k out of n Boolean variables. We give an algorithm for learning such functions from uniform random examples which runs in time roughly (nk)ω/(ω + 1), where ω is the matrix multiplication exponent. We thus obtain the first polynomial factor improvement on the naive nk time bound which can be achieved via exhaustive search. Our algorithm and analysis exploit new structural properties of Boolean functions.