Learning with imprecise probabilities as model selection and averaging

Abstract

This paper presents a general framework for learning with imprecise probabilities, consisting of a hierarchical approach with two sets of parameters. In the top set we have imprecise information, and conditioned on this set we have precise Bayesian information about the other set of parameters. Given a set of observations, the information about both sets of parameters is updated by conditioning, and a model selection method is applied to compute a reduced top set. This model selection method is based on decisions with imprecise probabilities. It will be shown that many existing approaches can be fitted in this general procedure, and a theoretical justification will be provided. Finally, the method will be applied to the problem of learning credal networks.