
[full paper] 
Rasa Jurgelenaite, Peter Lucas
The assessment of a probability distribution associated with a Bayesian network is a challenging task, even if its topology is sparse. Special probability distributions based on the notion of causal independence have therefore been proposed, as these allow defining a joint probability distribution in terms of Boolean combinations of local distributions. However, for very large networks even this approach becomes infeasible: in Bayesian networks which need to model a large number of interactions among causal mechanisms, such as in fields like genetics or immunology, it is necessary to further reduce the number of parameters that need to be assessed. Similar arguments apply to the modelling of temporal processes, which also involves large numbers of interactions among variables. In this paper, we propose using equivalence classes of binomial distributions as a means to define very large Bayesian networks. We analyse the behaviours obtained by using different symmetric Boolean functions with these probability distributions as a means to model joint interactions. Some surprisingly complicated behaviours are obtained in this fashion, and their intuitive basis is examined.
Keywords: Bayesian networks, causal independence, parameter estimation, knowledge representation, probability theory
Citation: Rasa Jurgelenaite, Peter Lucas: Parameter Estimation in Large Causal Independence Models. In R.López de Mántaras and L.Saitta (eds.): ECAI2004, Proceedings of the 16th European Conference on Artificial Intelligence, IOS Press, Amsterdam, 2004, pp.10371038.