Triangulation of Graphs -- Algorithms Giving Small Total State Space

The problem of achieving small total state space for triangulated belief graphs (networks) is considered. It is an NP-complete problem to find a triangulation with minimum state space. Our interes

Optimal Decomposition of Probabilistic Networks by Simulated Annealing

This paper investigates the applicability of a Monte Carlo technique known as `simulated annealing' to achieve optimum or sub-optimum decompositions of probabilistic networks under bounded resources. High-quality decompositions are essential for performing efficient inference in probabilistic networks. Optimum decomposition of probabilistic networks is known to be NP-hard (Wen 1990). The paper proves that cost-function changes can be computed locally, which is essential to the efficiency of the annealing algorithm. Pragmatic control schedules which reduce the running time of the annealing algorithm are presented and evaluated. Apart from the conventional temperature parameter, these schedules involve the radius of the search space as a new control parameter. The evaluation suggests that the inclusion of this new parameter is important for the success of the annealing algorithm for the present problem

Approximation of Bayesian networks through edge removals

Due to the general inherent complexity of inference in Bayesian networks, the need to compromise the exactitude of inference arises frequently. A scheme for reduction of complexity by enforcing additional conditional independences is investigated. The enforcement of independences is achieved through edge removals in a triangulated graph. The removal of a single edge may imply an enormous reduction of complexity, since other edges may become superuous by its removal. The approximation scheme presented has several appealing features. Most notably among these, a bound on the overall approximation error can be computed locally, the bound on the error by a series of approximations equals the sum of the bounds of the errors of the individual approximations, and the influence of an approximation attenuates with increasing `distance' from edge removed. The scheme compares in some cases very favorably with the approximation method suggested by Jensen & Andersen (1990)

HUGS: Combining Exact Inference and Gibbs Sampling in Junction Trees

Dawid, Kjærulff & Lauritzen (1994) provided a preliminary description of a hybrid between Monte-Carlo sampling methods and exact local computations in junction trees. Utilizing the strengths of both methods, such hybrid inference methods has the potential of expanding the class of problems which can be solved under bounded resources as well as solving problems which otherwise resist exact solutions. The paper provides a detailed description of a particular instance of such a hybrid scheme; namely, combination of exact inference and Gibbs sampling in discrete Bayesian networks. We argue that this combination calls for an extension of the usual message passing scheme of ordinary junction trees