Large margin case-based reasoning

The central problem in case based reasoning (CBR) is to infer a solution for a new problem-instance by using a collection of existing problem-solution cases. The basic heuristic guiding CBR is the hypothesis that similar problems have similar solutions. CBR has been often criticized for lacking a sound theoretical basis, and there has only recently been some attempts at formalizing CBR in a theoretical framework, including work by Hullermeier who made the link between CBR and the probably approximately correct (PAC) theoretical model of learning in his `case-based inference' (CBI) formulation. In this paper we present a new framework of CBI which models it as a multi-category classification problem. We use a recently-developed notion of geometric margin of classification to obtain generalization error bounds.