The dependency structure of a multivariate binary data set is investigated in terms of entropies. Classes of efficient condition variables are defined, and conditional independence statements defining the structure of a multivariate Bernoulli distribution are shown to be obtainable from such classes. A graphical method of representing the dependency structure based on the maximally informative outcomes of efficient condition variables is introduced. A simultaneous inference method based on sequential likelihood ratio tests is suggested for finding the classes of graphical models consistent with a set of empirical observations.

 Key words: Conditional Independence, Entropy, Graphical Models, Information Divergence, Multivariate Bernoulli distributions, Prediction. 

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Last update: 1997-12-16 / KH