Knowledge representation and inference in similarity networks and Bayesian multinets

Reviewer: Friedrich Gebhardt

A Bayesian network is a directed acyclic graph assigning a node to each statistical variable and a directed arc to each direct (causal) dependency. The graph shows whether two sets of variables are independent, or independent given the values of a third set of variables. If the prior probabilities of the root nodes (nodes without an incoming arc) and the conditional probabilities of each node—given the values of the variables corresponding to the incoming arcs—are known, all probabilities can be computed. Given, in addition, the observed values of some variables, the posterior probabilities of the root nodes can also be computed, in principle; however, the inference is NP-hard. Sometimes two variables are dependent given certain values of a root node, but independent given other values. Then several simplifications are possible through construction of separate, but simpler, Bayesian networks for certain distinct or overlapping sets of values of the root variable. This not only makes computations easier; it also saves having to know (or guess) certain conditional probabilities. Other extensions concern a nonroot variable, or two or more root variables.