COMPUTING MARGINAL PROBABILITIES IN CAUSAL MULTIWAY TREES GIVEN INCOMPLETE INFORMATION

Causal networks are structures within which recently established techn iques can be used to compute marginal probabilities. For these techniq ues to work, all the causal information implied by a particular networ k must be available. If some of the causal information is missing, Max imum Entropy could be used to provide these values in a minimally prej udiced manner. Unfortunately, the general problem of maximising Entrop y is NP-complete. However, the authors have already shown that a Maxim um Entropy approach to probabilistic reasoning is not intractable for causal information which can be represented by a binary tree. This pap er extends that result by proving that, given a multiway tree of causa l information (e.g. as required by Pearl's technique), the probability of the marginals can be found in linear space and time using Maximum Entropy. Further, it is shown that a simple algorithm can be used to e stimate missing information in a causal multiway tree and hence enable existing methods to be used in a situation when they otherwise could not have been. If this work can be extended to more general causal net works it would enhance existing techniques.