Maximal-margin case-based inference

The central problem in case-based reasoning (CBR) is to produce a solution for a new problem instance by using a set of existing problem-solution cases. The basic heuristic guiding CBR is the assumption 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 developing a theoretical framework, including recent work by Hullermeier, who made a link between CBR and the probably approximately correct (or PAC) probabilistic 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.