Representing and Solving Influence Diagram in Multi-Criteria Decision Making: A Loopy Belief Propagation Method

Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data mining. Influence diagrams provide a compact technique to represent problems of decision making especially multi-criteria decision making (MCDM) under uncertainty. As a number of nodes in the network increases, computing exact solutions and making optimal decision becomes computationally intractable. Approximate solution becomes more efficient in term of the performance of execution and the storage space. Loopy belief propagation is the alternative way for approximate solution and is presented in this paper. A solution is approximated where high-probability actions under the policy have a high utility. Actions are then selected which have a high probability under the approximating policy. The loopy belief propagation method is shown to compare favorably to exact methods.