The complexity of Boolean functions
The complexity of Boolean functions
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Exploiting causal independence in Bayesian network inference
Journal of Artificial Intelligence Research
Modelling treatment effects in a clinical Bayesian network using Boolean threshold functions
Artificial Intelligence in Medicine
Linking Bayesian networks and PLS path modeling for causal analysis
Expert Systems with Applications: An International Journal
Improving the therapeutic performance of a medical bayesian network using noisy threshold models
ISBMDA'05 Proceedings of the 6th International conference on Biological and Medical Data Analysis
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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 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. 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.