Year: 2008
Type: preprint
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 time of n^k * poly(n,2^k), 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,2^k,γ^{-k}). More generally, given access to t <= k different product distributions, the functions may be learned in time n^{k/t} * poly(n,2^k,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.
Source: arXiv (Cornell University)
Authors: Arpe, Jan, Mossel, Elchanan
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2953390946