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Pittsburgh, Pennsylvania, USA

Oct. 23, 2005 to Oct. 25, 2005

ISBN: 0-7695-2468-0

pp: 11-20

Adam Tauman Kalai , TTI-Chicago

Adam R. Klivans , UT-Austin

Yishay Mansour , Tel Aviv University

Rocco A. Servedio , Columbia University

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/SFCS.2005.13

ABSTRACT

<p>We give the first algorithm that (under distributional assumptions) efficiently learns halfspaces in the notoriously difficult agnostic framework of Kearns, Schapire, & Sellie, where a learner is given access to labeled examples drawn from a distribution, without restriction on the labels (e.g. adversarial noise). The algorithm constructs a hypothesis whose error rate on future examples is within an additive \varepsilon of the optimal halfspace, in time poly(n) for any constant \varepsilon > 0, under the uniform distribution over {-1,1}^n or the unit sphere in R^n, as well as under any log-concave distribution over R^n. It also agnostically learns Boolean disjunctions in time b^2 (\sqrt n) with respect to any distribution. The new algorithm, essentially L1 polynomial regression, is a noise-tolerant arbitrary-distribution generalization of the "low-degree" Fourier algorithm of Linial, Mansour, & Nisan. We also give a new algorithm for PAC learning halfspaces under the uniform distribution on the unit sphere with the current best bounds on tolerable rate of "malicious noise."</p>

INDEX TERMS

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CITATION

Adam Tauman Kalai,
Adam R. Klivans,
Yishay Mansour,
Rocco A. Servedio,
"Agnostically Learning Halfspaces",

*FOCS*, 2005, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2005, pp. 11-20, doi:10.1109/SFCS.2005.13