Credal model averaging: An extension of Bayesian model averaging to imprecise probabilities

Abstract

We deal with the arbitrariness in the choice of the prior over the models in Bayesian model averaging (BMA), by modelling prior knowledge by a set of priors (i.e., a prior credal set). We consider Dash and Cooper's BMA applied to naive Bayesian networks, replacing the single prior over the naive models by a credal set; this models a condition close to prior ignorance about the models, which leads to credal model averaging (CMA). CMA returns an indeterminate classification, i.e., multiple classes, on the instances for which the learning set is not informative enough to smooth the effect of the choice of the prior. We give an algorithm to compute exact credal model averaging for naive networks. Extensive experiments show that indeterminate classifications preserve the reliability of CMA on the instances which are classified in a prior-dependent way by BMA. © 2008 Springer-Verlag Berlin Heidelberg.