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Paper No. 09-07

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PA Thwaites, G Freeman and JQ Smith

Chain Event Graph MAP model selection

Abstract: When looking for general structure from a finite discrete data set it is quite common to search over the class of Bayesian Networks (BNs). The class of Chain Event Graph (CEG) models is however much more expressive and is particularly suited to depicting hypotheses about how situations might unfold. The CEG retains many of the desirable qualities of the BN. In particular it admits conjugate learning on its conditional probability parameters using product Dirichlet priors. The Bayes Factors associated with different CEG models can therefore be calculated in an explicit closed form, which means that search for the maximum a posteriori (MAP) model in this class can be enacted by evaluating the score function of successive models and optimizing. As with BNs, by choosing an appropriate prior over the model space, the conjugacy property ensures that this score function is linear in the different components of the CEG model. Local search algorithms can therefore be devised which unveil the rich class of candidate explanatory models, and allow us to select the most appropriate. In this paper we concentrate on this discovery process and upon the scoring of models within this class.