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.
[1]
Prakash P. Shenoy,et al.
Axioms for probability and belief-function proagation
,
1990,
UAI.
[2]
Prakash P. Shenoy,et al.
Local Computation in Hypertrees
,
1991
.
[3]
Richard E. Neapolitan,et al.
Probabilistic reasoning in expert systems - theory and algorithms
,
2012
.
[4]
David J. Spiegelhalter,et al.
Local computations with probabilities on graphical structures and their application to expert systems
,
1990
.
[5]
A. Hasman,et al.
Probabilistic reasoning in intelligent systems: Networks of plausible inference
,
1991
.
[6]
Judea Pearl,et al.
Fusion, Propagation, and Structuring in Belief Networks
,
1986,
Artif. Intell..