Uncertain Reasoning In Bayesian Networks

Bayesian network (BN, also known as belief network or casual network) is a mathematical model based on probability theory. It is a tool developed in Artificial Intelligence for modeling probabilistic interdependencies in complex problems and supporting, uncertainty reasoning and data analysis. BN has been recognized as one of the most efficient theoretical models in representation and reasoning of uncertainty knowledge, and has applied in many areas. However, there are still many problems to be resolved for Bayesian networks in knowledge integration and reasoning, e.g. belief update under uncertain information.In this dissertation, we first discussed properties and features of different existing knowledge integration algorithms, such as IPFP (iterative proportional fitting procedure) and other IPFP based algorithms, e.g. CIPFP (conditional IPFP), CC-IPFP, GEMA etc. Then a novel algorithm, SMOOTH, was proposed. The new algorithm extends original IPFP by bi-directional modification of probabilistic constraints and target joint probability distribution during the iterations, thus it converges for both consistent and inconsistent constraints. Experiment results show that, compared with existing algorithms, SMOOTH has stable and fast convergence, and can be accelerated by adjusting its smooth ratio.Knowledge integration algorithms based on IPFP work on joint probability distributions, thus it can not be used directly in Bayesian networks. For this problem, we introduced the E-IPFP algorithm proposed by Peng and Ding. A formal convergence proof of E-IPFP under consistent probabilistic constraints was given. In addition, an improved method was proposed by integrating E-IPFP and SMOOTH to deal with inconsistent constraints. Experiment results show that, the improved algorithm can handle not only inconsistency among probabilistic constraints but also inconsistency between constraints and the BN structure.Algorithms for Bayesian network belief update under uncertain evidences were also discussed. Classification and features of different uncertain evidences are discussed thoroughly. Also we introduced the equivalence of different belief update algorithms (Jeffrey's Rule, Virtual Evidence Method, and IPFP) for single uncertain evidence. Based on Pan and Peng's work, the algorithm, BN-IPFP, with its convergence proof was discussed for multiple evidences. We expanded BN-IPFP by combining it with SMOOTH, and the expanded algorithm can deal with not only multiple uncertain evidences but also inconsistent evidences. Both theoretical and experimental convergence proof are discussed thorough.Finally, we discussed the application of Bayesian network to modeling and reasoning with uncertainty in Semantic Web ontologies. The BayesOWL framework was extended to support converting general ontologies (e.g. OWL DL) to BNs, and a convention based on OWL language was proposed to represent probabilistic knowledge for ontology classes and interclass relations. Knowledge integration algorithms we developed are used to integrate probabilistic knowledge into converted BN. A prototype system of the extended BayesOWL framework was implemented with its APIs available for researchers on similar research areas.