Objective Bayesian Nets for Integrating Consistent Datasets

This paper addresses a data integration problem: given several mutually consistent datasetseach of which measures a subset of the variables of interest, how can one construct a probabilisticmodel that fits the data and gives reasonable answers to questions which are under-determined bythe data? Here we show how to obtain a Bayesian network model which represents the uniqueprobability function that agrees with the probability distributions measured by the datasets and oth-erwise has maximum entropy. We provide a general algorithm, OBN-cDS, which offers substantialefficiency savings over the standard brute-force approach to determining the maximum entropyprobability function. Furthermore, we develop modifications to the general algorithm which en-able further efficiency savings but which are only applicable in particular situations. We show thatthere are circumstances in which one can obtain the model (i) directly from the data; (ii) by solvingalgebraic problems; and (iii) by solving relatively simple independent optimisation problems.