Representation of Bayesian Networks as Relational Databases

A Bayesian network can be regarded as a summary of a domain expert’s experience with an implicit population. A database can be regarded as a detailed documentation of such an experience with an explicit population. This connection between Bayesian networks and databases is well recognized and have been pursued for knowledge acquisition [1, 2, 11]. Existing databases are treated as information resources. Automatic generation of Bayesian networks from databases are studied as a way to bypass the knowledge acquisition bottleneck. Once Bayesian networks are generated, databases are regarded as no longer relevant to the evidential reasoning process in Bayesian networks. Much evidence suggests that even deeper connection between Bayesian networks and relational databases exists. Relational databases manipulate tables of tuples, and Bayesian networks manipulate tables of probabilities. Relational databases answer queries that involve attributes in multiple relations by joining the relations and then projecting to the set of target attributes. In Bayesian networks, joint distributions are defined by products of local distributions, and belief updating [9] computes the marginalization of joint distributions. Relational databases make use of junction (join) trees in database design [7]. Multiply connected Bayesian networks are transformed into junction trees [5] or junction forests [13] to achieve inference efficiency. Scenario based explanation [3] in Bayesian networks uses the most likely configurations, which are equavalent to the universal tuples that repeat most frequently if we allow repetition in the database. Sequential updating (learning) of conditional probabilities [10, 12] in Bayesian networks makes use of new cases which are new tuples in databases. The paper explores the connection between Bayesian networks and relational databases. We presents a representation and inference framework of Bayesian networks using relational databases. The framework is based on the junction tree representation of Bayesian networks [5]. We show that with some minor extension to the conventional relational database model, it can be used to represent Bayesian networks and to perform probabilistic inference. This unified framework formally reveals the close relationship