PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Learning Kernel-Based Halfspaces with the Zero-One Loss
Shai Shalev-Shwartz, Ohad Shamir and Karthik Sridharan
In: COLT 2010(2010).

Abstract

We describe and analyze a new algorithm for agnostically learning kernel-based halfspaces with respect to the \emph{zero-one} loss function. Unlike most previous formulations which rely on surrogate convex loss functions (e.g. hinge-loss in SVM and log-loss in logistic regression), we provide finite time/sample guarantees with respect to the more natural zero-one loss function. The proposed algorithm can learn kernel-based halfspaces in worst-case time $\poly(\exp(L\log(L/\epsilon)))$, for $\emph{any}$ distribution, where $L$ is a Lipschitz constant (which can be thought of as the reciprocal of the margin), and the learned classifier is worse than the optimal halfspace by at most $\epsilon$. We also prove a hardness result, showing that under a certain cryptographic assumption, no algorithm can learn kernel-based halfspaces in time polynomial in $L$.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:6957
Deposited By:Ohad Shamir
Deposited On:20 June 2010