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Advances in Knowledge Discovery and Data Mining

Volume 5476 of the series Lecture Notes in Computer Science pp 208-219

Interval Data Classification under Partial Information: A Chance-Constraint Approach

  • Sahely BhadraAffiliated withCarnegie Mellon UniversityDept. of Computer Science and Automation, Indian Institute of Science
  • , J. Saketha NathAffiliated withCarnegie Mellon UniversityMINERVA Optimization center, Faculty of Industrial Engg. and Management, Technion
  • , Aharon Ben-TalAffiliated withCarnegie Mellon UniversityMINERVA Optimization center, Faculty of Industrial Engg. and Management, Technion
  • , Chiranjib BhattacharyyaAffiliated withCarnegie Mellon UniversityDept. of Computer Science and Automation, Indian Institute of Science

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Abstract

This paper presents a Chance-constraint Programming approach for constructing maximum-margin classifiers which are robust to interval-valued uncertainty in training examples. The methodology ensures that uncertain examples are classified correctly with high probability by employing chance-constraints. The main contribution of the paper is to pose the resultant optimization problem as a Second Order Cone Program by using large deviation inequalities, due to Bernstein. Apart from support and mean of the uncertain examples these Bernstein based relaxations make no further assumptions on the underlying uncertainty. Classifiers built using the proposed approach are less conservative, yield higher margins and hence are expected to generalize better than existing methods. Experimental results on synthetic and real-world datasets show that the proposed classifiers are better equipped to handle interval-valued uncertainty than state-of-the-art.