Boosting in the Presence of Noise.
A. Kalai and R. Servedio.
Journal of Computer and System Sciences 71(3), 2005, pp. 266-290 (special issue for STOC, FOCS, and COLT 2003).
Preliminary version in 35th Annual Symposium on Theory of Computing (STOC), 2003, pp. 196-205.


Boosting algorithms are procedures that ``boost'' low accuracy weak learning algorithms to achieve arbitrarily high accuracy. Over the past decade boosting has been widely used in practice and has become a major research topic in computational learning theory. In this paper we study boosting in the presence of random classification noise, giving both positive and negative results.

We show that a modified version of a boosting algorithm due to Mansour and McAllester \cite{MansourMcAllester:02} can achieve accuracy arbitrarily close to the noise rate. We also give a matching lower bound by showing that no efficient black-box boosting algorithm can boost accuracy beyond the noise rate (assuming that one-way functions exist). Finally, we consider a variant of the standard scenario for boosting in which the ``weak learner'' satisfies a slightly stronger condition than the usual weak learning guarantee. We give an efficient algorithm in this framework which can boost to arbitrarily high accuracy in the presence of classification noise.

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