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Published Articles >> Table of Contents >> Abstract
46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
pp. 11-20
Agnostically Learning Halfspaces
Adam Tauman Kalai, TTI-Chicago
Adam R. Klivans, UT-Austin
Yishay Mansour, Tel Aviv University
Rocco A. Servedio, Columbia University
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DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/SFCS.2005.13
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| Abstract |
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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."
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Citation:
Adam Tauman Kalai, Adam R. Klivans, Yishay Mansour, Rocco A. Servedio,
"Agnostically Learning Halfspaces,"
focs,
pp. 11-20,
46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05),
2005
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