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

This paper presents a novel methodology for constructing maximum-margin classifiers which are robust to interval-valued uncertainty in examples. The idea is to employ chance-constraints which ensure that the uncertain examples are classified correctly with high probability. The key novelty is in employing Bernstein bounding schemes to relax the resulting chance-constrained program as a convex second order cone program. The Bernstein based relaxations presented in the paper require the knowledge of support and mean of the uncertain examples alone and make no assumptions on distributions regarding the underlying uncertainty. Classifiers built using the proposed methodology model interval-valued uncertainty in a less conservative fashion 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.