The relational database theory of bayesian networks
Man Sang Wong, Cory J. Butz · 2000
Based on the elegant theory of relational databases, the present investigation establishes a unified model for both relational databases and Bayesian networks. This is in contradiction to the argument that relational databases and Bayesian networks are different, where it was shown that the implication problem does not coincide for embedded multivalued dependency (EMVD) and probabilistic conditional independence (CI). The main result of this thesis, however, is that the implication problem coincides on the solvable subclasses of EMVD and CI, but differs on the unsolvable general classes of EMVD and CI. This means that there is no practical difference between relational databases and Bayesian networks, since only the solvable subclasses are useful in the design of both of these knowledge systems. A unified model provides the opportunity for cross-research. Recently, attempts have been made to generalize the standard Bayesian network model with contextual dependencies, an object-oriented Bayesian network model, and a multi-agent Bayesian network model. In this thesis, we demonstrate the usefulness of our unified model by making significant contributions to these extensions. By drawing from the highly developed relational database model, we propose more general probabilistic dependencies as well as several consistency results in the object-oriented and multi-agent models.