
Statistics Papers
Document Type
Journal Article
Date of this Version
3-2010
Publication Source
Combinatorics, Probability and Computing
Volume
19
Issue
2
Start Page
183
Last Page
199
DOI
10.1017/S0963548309990277
Abstract
We study the problem of learning k-juntas given access to examples drawn from a number of different product distributions. Thus we wish to learn a function f: {−1, 1}n → {−1, 1} that depends on k (unknown) coordinates. While the best-known algorithms for the general problem of learning a k-junta require running times of nk poly(n, 2k), we show that, given access to k different product distributions with biases separated by γ > 0, the functions may be learned in time poly(n, 2k, γ−k). More generally, given access to t ≤ k different product distributions, the functions may be learned in time nk/tpoly(n, 2k, γ−k). Our techniques involve novel results in Fourier analysis, relating Fourier expansions with respect to different biases, and a generalization of Russo's formula.
Keywords
learning juntas, PAC learning, biased product distributions, Fourier analysis of Boolean functions, Russo’s formula
Recommended Citation
Arpe, J., & Mossel, E. (2010). Multiple Random Oracles Are Better Than One. Combinatorics, Probability and Computing, 19 (2), 183-199. http://dx.doi.org/10.1017/S0963548309990277
Date Posted: 27 November 2017
This document has been peer reviewed.
Comments
At the time of publication, author Elchanan Mossel was affiliated with the University of California, Berkeley. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.
The postprint version of this article, Multiple Random Oracles Are Better Than One, is published in its final form under the title Application of a Generalization of Russo's Formula to Learning from Multiple Random Oracles.