Boosting and support vector machines as optimal separators

Saharon Rosset; Ji Zhu; Trevor J. Hastie

doi:10.1117/12.497492

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13 January 2003 Boosting and Support Vector Machines as Optimal Separators

Saharon Rosset, Ji Zhu, Trevor J. Hastie

Proceedings Volume 5010, Document Recognition and Retrieval X; (2003) https://doi.org/10.1117/12.497492
Event: Electronic Imaging 2003, 2003, Santa Clara, CA, United States

Abstract

In this paper we study boosting methods from a new perspective. We build on recent work by Efron et al. to show that boosting approximately (and in some cases exactly) minimizes its loss criterion with an L₁ constraint. For the two most commonly used loss criteria (exponential and logistic log-likelihood), we further show that as the constraint diminishes, or equivalently as the boosting iterations proceed, the solution converges in the separable case to an “L₁-optimal” separating hyper-plane. This “L₁-optimal” separating hyper-plane has the property of maximizing the minimal margin of the training data, as de£ned in the boosting literature. We illustrate through examples the regularized and asymptotic behavior of the solutions to the classifcation problem with both loss criteria.

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Saharon Rosset, Ji Zhu, and Trevor J. Hastie "Boosting and Support Vector Machines as Optimal Separators", Proc. SPIE 5010, Document Recognition and Retrieval X, (13 January 2003); https://doi.org/10.1117/12.497492

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