Compact approximations to Bayesian predictive distributions
ICML '05 Proceedings of the 22nd international conference on Machine learning
Learning dynamic Bayesian network models via cross-validation
Pattern Recognition Letters
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
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Given a set of possible models for variables X and a set ofpossible parameters for each model, the Bayesian “estimate” of theprobability distribution for X given observed data is obtained byaveraging over the possible models and their parameters. An often-usedapproximation for this estimate is obtained by selecting a single modeland averaging over its parameters. The approximation is useful becauseit is computationally efficient, and because it provides a model thatfacilitates understanding of the domain. A common criterion for modelselection is the posterior probability of the model. Another criterionfor model selection, proposed by San Martini and Spezzafari (1984), isthe predictive performance of a model for the next observation to beseen. From the standpoint of domain understanding, both criteria areuseful, because one identifies the model that is most likely, whereasthe other identifies the model that is the best predictor of the nextobservation. To highlight the difference, we refer to theposterior-probability and alternative criteria as the scientificcriterion (SC) and engineering criterion (EC),respectively. Whenwe are interested in predicting the next observation, the model-averagedestimate is at least as good as that produced by EC, which itself is atleast as good as the estimate produced by SC. We show experimentallythat, for Bayesian-network models containing discrete variables only,the predictive performance of the model average can be significantlybetter than those of single models selected by either criterion, andthat differences between models selected by the two criterion can besubstantial.