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In this paper we derive an explicit formula for calculating the marginallikelihood of a given factorization of a categorical dataset. Since themarginal likelihood is proportional to the posterior probability of thefactorization, these likelihoods can be used to order all possiblefactorizations and select the "best" way to factor the overall distributionfrom which the dataset is drawn. The best factorization can then be used toconstruct a Bayes classifier which benefits from factoring out mutuallyindependent sets of variables.

Factoring Multidimensional Data to Create a Sophisticated Bayes Classifier