Fusion, propagation, and structuring in belief networks
Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in expert systems: theory and algorithms
Probabilistic reasoning in expert systems: theory and algorithms
Axioms for probability and belief-function propagation
Readings in uncertain reasoning
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This paper introduces a mathematical model of a probability propagation in hypertrees. Suppose that a probability measure P on a set of random variables factors on a hypertree. That is, there is for each node a non-negative function \p of the configurations of the random variables represented by the node such that P is the product of these functions: P = \7P \p. Each pair (\3Y, {\p}) forms a factorization network of P, where \3Y is a Markov-tree representation of the hypertree. This paper introduces a local computation of the factorization network relative to an arbitrary subset of random variables, and derives the invariant properties of the network. Based on the invariance, the marginal of P on the given subset of random variables can be computed by propagating the local computation in the network.