Loopy Belief Propagation Application for Advanced Decision Making Models

Abstract

Loopy Belief propagation (LBP) is a technique for distributed inference in performing approximate inference on arbitrary graphical models. In this paper, we propose an extended influence diagram with loopy belief propagation technique to solve the advanced decision making problems, especially the multi-criteria decision making (MCDM) in term of uncertain criteria. When a number of nodes is increasing in the network, solving for exact solutions and making optimal decision becomes complicated and time consuming. The belief propagation is an efficient way to solve inference problems by propagating local messages around neighborhoods. In this paper, we will focus on the principle of loopy belief propagation, and its applications in advanced decision making problems. Loopy belief propagation is another choice for solving the advance decision making problem in order to get approximate solution and is selected to present in this paper. A solution is approximated which a high probability action under the preference criteria and high utility. In addition, the comparison between the loopy belief propagation method including other approximated method and the exact methods based on the prediction and the running time is shown in this research. The Belief propagation algorithm is well studied in the literature and is currently used in order to analyze systems which are modeled by decision support system. The belief propagation algorithm allows us to get the marginal of all variables, with a computational time only in the linear in the number of variables. This algorithm can be used in a vast range of decision making model areas, especially, in Multi Criteria Decision-Making Method (MCDM). This method is about to make preference decisions over the available alternatives based on multiple and conflicting criteria (1). In previous research, the model of decision-making is complicated because there are a lot of choices to choose from and the people have many factors to be considered while making the decision Therefore, the advance techniques for solving the decision need to be investigate in order to get the optimal solution or the to make the right decision for decision makers. Bayesian network and Influence diagram (ID) are developed in the field of artificial intelligence (AI) for representing and reasoning under uncertainty. In the model, decision criteria and factors are considered as random variables and represented as node in the network. The network structure associated with conditional probability tables and each node which provide a representation of the joint probability distribution of all variables. There are some algorithms that have been developed for probabilistic inference like probabilistic inference, Bayesian network. This paper focuses on the method for solving advanced decision making problems and presents our current research for developing an approximate algorithm for solving advanced decision making problems. Nowadays, it appears many algorithms in both exact and approximate, for solving advanced decision making problems. Normally, researchers like to use approximate methods such as Monte Carlo (MCMC) simulation, sampling method, variational method, and so on for solving the decision problems. However, those methods are very complicated and hard to get both exact and approximated solutions. Sallans (12) found that the sampling method and MCMC method is good solution when the number of nodes is increase or in the large the network. However, MCMC and sampling method have a convergence problem and they can apply for a limited in some networks (14). In this research loopy belief propagation is proposed for finding the solution to evaluate the advanced decision making problems. It has been used for approximate inference in a wide variety of many model especially in Bayesian network and influence diagram model (14). The loopy propagation method is compared to others methods in prediction and performance of running time. Therefore, the likelihood weight method, junction tree method and Markov Chain Monte Carlo (MCMC) method are selected for experiment in this paper.