Knowledge Engineering for Bayesian Networks: How Common Are Noisy-MAX Distributions in Practice?

One problem faced in knowledge engineering for Bayesian networks (BNs) is the exponential growth of the number of parameters in their conditional probability tables (CPTs). The most common practical solution is the application of the so-called canonical gates and, among them, the noisy-or (or their generalization, the noisy-MAX) gates, which take advantage of the independence of causal interactions and provide a logarithmic reduction of the number of parameters required to specify a CPT. In this paper, we propose an algorithm that fits a noisy-MAX distribution to an existing CPT, and we apply this algorithm to search for noisy-MAX gates in three existing practical BN models: Alarm, Hailfinder, and Hepar II. We show that the noisy-MAX gate provides a surprisingly good fit for as many as 50% of CPTs in two of these networks. We observed this in both distributions elicited from experts and those learned from data. The importance of this finding is that it provides an empirical justification for the use of the noisy-MAX gate as a powerful knowledge engineering tool.