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Efficient Methods for Robust Classification Under Uncertainty in Kernel Matrices

Ben-Tal, Aharon and Bhadra, Sahely and Bhattacharyya, Chiranjib and Nemirovski, Arkadi (2012) Efficient Methods for Robust Classification Under Uncertainty in Kernel Matrices. In: JOURNAL OF MACHINE LEARNING RESEARCH, 13 . pp. 2923-2954.

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In this paper we study the problem of designing SVM classifiers when the kernel matrix, K, is affected by uncertainty. Specifically K is modeled as a positive affine combination of given positive semi definite kernels, with the coefficients ranging in a norm-bounded uncertainty set. We treat the problem using the Robust Optimization methodology. This reduces the uncertain SVM problem into a deterministic conic quadratic problem which can be solved in principle by a polynomial time Interior Point (IP) algorithm. However, for large-scale classification problems, IP methods become intractable and one has to resort to first-order gradient type methods. The strategy we use here is to reformulate the robust counterpart of the uncertain SVM problem as a saddle point problem and employ a special gradient scheme which works directly on the convex-concave saddle function. The algorithm is a simplified version of a general scheme due to Juditski and Nemirovski (2011). It achieves an O(1/T-2) reduction of the initial error after T iterations. A comprehensive empirical study on both synthetic data and real-world protein structure data sets show that the proposed formulations achieve the desired robustness, and the saddle point based algorithm outperforms the IP method significantly.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to MICROTOME PUBL,USA
Keywords: robust optimization;uncertain classification;kernel functions
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Francis Jayakanth
Date Deposited: 13 Feb 2013 10:37
Last Modified: 13 Feb 2013 10:37
URI: http://eprints.iisc.ac.in/id/eprint/45795

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