Probabilistic modeling and reasoning in multiagent decision systems

Ph.DDOCTOR OF PHILOSOPH

A Polynomial transformation from vertex cover problem to exact inference problem in bayesian belief networks

Exact Inference problem in Belief Networks has been well studied in the literature and has various application areas. In this thesis, a polynomial time transformation from Vertex Cover Problem to Exact Inference problem in Belief Networks is proposed and proved. To understand and see the development of the transformation, some well-known transformations about Vertex Cover Problem and Exact Inference, are introduced. By using the transformation proposed, some Vertex Cover problems are converted to Exact Inference Problems and solved by softwares using the algorithms of Exact Inference

Decision Making under Uncertainty through Extending Influence Diagrams with Interval-valued Parameters

Influence Diagrams (IDs) are one of the most commonly used graphical and mathematical decision models for reasoning under uncertainty. In conventional IDs, both probabilities representing beliefs and utilities representing preferences of decision makers are precise point-valued parameters. However, it is usually difficult or even impossible to directly provide such parameters. In this paper, we extend conventional IDs to allow IDs with interval-valued parameters (IIDs), and develop a counterpart method of Copper’s evaluation method to evaluate IIDs. IIDs avoid the difficulties attached to the specification of precise parameters and provide the capability to model decision making processes in a situation that the precise parameters cannot be specified. The counterpart method to Copper’s evaluation method reduces the evaluation of IIDs into inference problems of IBNs. An algorithm based on the approximate inference of IBNs is proposed, extensive experiments are conducted. The experimental results indicate that the proposed algorithm can find the optimal strategies effectively in IIDs, and the interval-valued expected utilities obtained by proposed algorithm are contained in those obtained by exact evaluating algorithms

Proceedings of the Fifth European Workshop on Probabilistic Graphical Models

Peer reviewe

Importance Sampling for Bayesian Networks: Principles, Algorithms, and Performance

Bayesian networks (BNs) offer a compact, intuitive, and efficient graphical representation of uncertain relationships among the variables in a domain and have proven their value in many disciplines over the last two decades. However, two challenges become increasingly critical in practical applications of Bayesian networks. First, real models are reaching the size of hundreds or even thousands of nodes. Second, some decision problems are more naturally represented by hybrid models which contain mixtures ofdiscrete and continuous variables and may represent linear or nonlinear equations and arbitrary probability distributions. Both challenges make building Bayesian network models and reasoning withthem more and more difficult.In this dissertation, I address the challenges by developing representational and computational solutions based on importance sampling. I First develop a more solid understanding of the properties of importance sampling in the context of Bayesian networks. Then, I address a fundamental question of importance sampling in Bayesian networks, the representation of the importance function. I derive an exact representation for the optimal importance function and propose an approximation strategy for therepresentation when it is too complex. Based on these theoretical analysis, I propose a suite of importance sampling-based algorithms for (hybrid) Bayesian networks. I believe the new algorithmssignificantly extend the efficiency, applicability, and scalability of approximate inference methods for Bayesian networks. The ultimate goal of this research is to help users to solve difficult reasoning problems emerging from complex decision problems in the most general settings

Automated clinical decision model construction from knowledge-based GLIF guideline models

Master'sMASTER OF ENGINEERIN

Glosarium Matematika

273 p.; 24 cm