On the Integration of Inconsistent Knowledge with Bayseian Networks

Incorporating or integrating new knowledge into existing knowledge bases (KBs) is critical for developing and maintaining the reliability and accuracy thereof. This thesis focuses on integrating pieces of discrete probabilistic knowledge, represented as low dimensional distributions (also called constraints), into an existing Bayesian network (BN) where the probabilistic dependency relations among the variables in these constraints are inconsistent with those captured by the network structure of the existing BN. In this situation, we say the constraints have structural inconsistencies with the BN. None of the existing methods for probabilistic knowledge integration deal with structural inconsistencies specifically. When such inconsistencies occur, these methods either do not converge or converge by modifying the constraints to remove these inconsistencies.

In this thesis we develop a theoretical framework and related methods to fill this gap. The contributions of this thesis are in three areas. First, we define structural inconsistency so it can be distinguished from other types of inconsistencies. Second, we develop a method, referred to as InconsId, to identify structural inconsistencies between a BN and a set of constraints. Third, we propose two classes of methods to overcome the structural inconsistencies by modifying the structure of the existing BN. The class of AddNode methods adapts the virtual evidence method of BN reasoning to solve the problem of integrating structurally inconsistent constraints with a BN. The class of AddLink methods addresses the same issue by compensating for the missing dependencies in the BN with added links. Variations of methods are developed in each class to balance the computational cost and solution quality. Additionally, both theoretical analysis and experiments are conducted to validate the effectiveness of these methods and compare their performance. At the end of this thesis, the developed framework and related methods are extended to solve a real-world problem of constructing a large BN from a set of small BNs.

By modifying the structure of the existing BN in a principled way, our work pioneers the research in the area of integrating structurally inconsistent constraints without sacrificing their integrity. Our research can be applied to a wide range of problems for knowledge integration with BNs without imposing structural restrictions on the inputs. Therefore, it may yield more accurate and more reliable knowledge models. It can also be extended to other related KB integration tasks such as KB merging.


ai, bayesian networks, knowledge representation

PhdThesis

University of Maryland, Baltimore County

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