Research and Development in Intelligent Systems XXII (PDF)

"SESSION 2: NETWORKS AND BIOLOGICALLV MOTIVATED AI (S. 132-133)

Exploring the Noisy Threshold Function in Designing Bayesian Networks*

Rasa Jurgelenaite, Peter Lucas and Tom Heskes Radboud University Nijmegen, Nijmegen, The Netherlands E-mail : {rasa.peterl.tomh}@cs.ru.nl

Abstract
Causal independence modelling is a well-known method both for reducing the size of probability tables and for explaining the underlying mechanisms in Bayesian networks. Many Bayesian network models incorporate causal independence assumptions; however, only the noisy OR and noisy AND, two examples of causal independence models, are used in practice. Their underlying assumption that either at least one cause, or all causes together, give rise to an effect, however, seems unnecessarily restrictive. In the present paper a new, more flexible, causal independence model is proposed, based on the Boolean threshold function. A connection is established between conditional probability distributions based on the noisy threshold model and Poisson binomial distributions, and the basic properties of this probability distribution are studied in some depth. The successful application of the noisy threshold model in the refinement of a Bayesian network for the diagnosis and treatment of ventilator-associated pneumonia demonstrates the practical value of the presented theory.

1 Introduction

Bayesian networks offer an appealing language for building models of domains with inherent uncertainty. However, the assessment of a probability distribution in Bayesian networks is a challenging task, even if its topology is sparse. This task becomes even more complex if the model has to integrate expert knowledge. While learning algorithms can be forced to take into account an experts view, for the best possible results the experts must be willing to reconsider their ideas in light of the models discovered structure.

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