Chance constrained uncertain classification via robust optimization

Ben-Tal, Aharon and Bhadra, Sahely and Bhattacharyya, Chiranjib and Nath, Saketha J (2011) Chance constrained uncertain classification via robust optimization. In: Mathematical Programming, 127 (1). pp. 145-173.

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Abstract

This paper studies the problem of constructing robust classifiers when the training is plagued with uncertainty. The problem is posed as a Chance-Constrained Program (CCP) which ensures that the uncertain data points are classified correctly with high probability. Unfortunately such a CCP turns out to be intractable. The key novelty is in employing Bernstein bounding schemes to relax the CCP as a convex second order cone program whose solution is guaranteed to satisfy the probabilistic constraint. Prior to this work, only the Chebyshev based relaxations were exploited in learning algorithms. Bernstein bounds employ richer partial information and hence can be far less conservative than Chebyshev bounds. Due to this efficient modeling of uncertainty, the resulting classifiers achieve higher classification margins and hence better generalization. Methodologies for classifying uncertain test data points and error measures for evaluating classifiers robust to uncertain data are discussed. Experimental results on synthetic and real-world datasets show that the proposed classifiers are better equipped to handle data uncertainty and outperform state-of-the-art in many cases.

Item Type:	Journal Article
Publication:	Mathematical Programming
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer.
Keywords:	Chance-constraints;Bernstein inequalities;Maximum-margin classification;SOCP
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	08 Apr 2011 07:22
Last Modified:	08 Apr 2011 07:22
URI:	http://eprints.iisc.ac.in/id/eprint/36569

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