An Axiomatic Framework for Bayesian and Belief-function Propagation
This work provides a foundational framework for probabilistic and belief-function computations, which is incremental as it generalizes existing methods.
The authors tackled the problem of exact local computation of marginals by proposing an axiomatic framework with variables and valuations, using combination and marginalization operators, and demonstrated its applicability to Bayesian and belief-function propagation.
In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the axioms. Next, we describe a propagation scheme for computing marginals of a valuation when we have a factorization of the valuation on a hypertree. Finally we show how the problem of computing marginals of joint probability distributions and joint belief functions fits the general framework.