PEBM: A Probabilistic Exemplar Based Model

A central problem in case based reasoning (CBR) is how to store and retrieve cases. One approach to this problem is to use exemplar based models, where only the prototypical cases are stored. However, the development of an ex-emplar based model (EBM) requires the solution of several problems: (i) how can a EBM be represented? (ii) given a new case, how can a suitable exemplar be retrieved? (iii) what makes a good exemplar? (iv) how can an EBM be learned incrementally? This paper develops a new model, called a probabilistic exemplar based model, that addresses these questions. The model utilizes Bayesian networks to develop a suitable representation and uses prob-abilistic propagation for assessing and retrieving exemplars when a new case is presented. The model learns incrementally by revising the exemplars retained and by updating the conditional probabilities required by the Bayesian network. The paper also presents the results of evaluating the model on three datasets. 1 Introduction Case Based Reasoning (CBR) is an approach that utilises past situations in an attempt to solve new problems. The basic CBR cycle involves retrieving cases that are similar to the current problem and utilising them to solve the current problem. This makes memory organisation and indexing a fundamental part of CBR systems. One approach is to store a flat database of cases and scan all the cases to identify the most similar cases. For applications where many more are involved, this simple organisation is considered to be slow [Kolodner, 1993]. A more sophisticated method is to partition the cases into clusters and organise them hierarchically. The hierarchy can then be searched more efficiently by following a path depending on the features of the new case. Different types of hierarchies have been proposed leading to different approaches. One approach is to use decision trees so that the leaf nodes contain the cases and where the internal nodes contain questions that can be used to partition the cases. So for example, systems like ReMind [Althoff et o/., 1995] provide a tree induction algorithm that can be used to avoid examining all the cases. This kind of approach is particularly useful when large databases of cases are already available. However, when cases are not available in advance, and the domain is not well defined this approach is more difficult to apply. Another approach is to use an abstraction hierarchy where each internal node is an abstraction …