TY - JOUR

T1 - Learning kernel-based halfspaces with the 0-1 loss

AU - Shalev-Shwartz, Shai

AU - Shamir, Ohad

AU - Sridharan, Karthik

PY - 2011

Y1 - 2011

N2 - We describe and analyze a new algorithm for agnostically learning kernel-based halfspaces with respect to the 0-1 loss function. Unlike most of the previous formulations, which rely on surrogate convex loss functions (e.g., hinge-loss in support vector machines (SVMs) and log-loss in logistic regression), we provide finite time/sample guarantees with respect to the more natural 0-1 loss function. The proposed algorithm can learn kernel-based halfspaces in worst-case time poly(exp(Llog(L/ε))), for 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 ε. 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.

AB - We describe and analyze a new algorithm for agnostically learning kernel-based halfspaces with respect to the 0-1 loss function. Unlike most of the previous formulations, which rely on surrogate convex loss functions (e.g., hinge-loss in support vector machines (SVMs) and log-loss in logistic regression), we provide finite time/sample guarantees with respect to the more natural 0-1 loss function. The proposed algorithm can learn kernel-based halfspaces in worst-case time poly(exp(Llog(L/ε))), for 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 ε. 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.

KW - Kernel methods

KW - Learning halfspaces

KW - Learning theory

UR - http://www.scopus.com/inward/record.url?scp=84855575451&partnerID=8YFLogxK

U2 - 10.1137/100806126

DO - 10.1137/100806126

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AN - SCOPUS:84855575451

SN - 0097-5397

VL - 40

SP - 1623

EP - 1646

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 6

ER -