Scoring Bayesian Networks with Informative, Causal and Associative Priors

A significant theoretical advantage of search-and-score methods for learning Bayesian Networks is that they can accept informative prior beliefs for each possible network, thus complementing the data. Currently however, there are limited practical ways of assigning priors to each possible network. In this paper, we present a method for assigning priors based on beliefs on the presence or absence of certain paths in the true network. Such beliefs correspond to knowledge about the possible causal and associative relations between a pair of variables X and Y. This type of knowledge naturally arises from prior experimental and observational datasets, among others. We show that incorporating such prior knowledge may not only improve the learning of the direction of the causal relations in the network, but also the learning of the network skeleton. This is particularly the case when sample size is low and thus prior knowledge increases in importance. Our approach is based on converting possibly-incoherent beliefs about marginals to joint distributions of priors by use of optimization theory.