DemocraticOP: A democratic way of aggregating Bayesian network parameters
When there are several experts in a specific domain, each may believe in a different Bayesian network (BN) representation of the domain. In order to avoid having to work with several BNs, it is desirable to aggregate them into a single BN. One way of finding the aggregated BN is to start by finding the structure, and then find the parameters. In this paper, we focus on the second step, assuming that the structure has been found by some previous method. DemocraticOP is a new way of combining experts' parameters in a model. The logic behind this approach is borrowed from the concept of democracy in the real world. We assume that there is a ground truth and that each expert represents a deviation from it - the goal is to try to find the ground truth based on the experts' opinions. If the experts do not agree, then taking a simple average of their opinions (as occurs in classical aggregation functions such as LinOP and LogOP) is flawed. Instead, we believe it is better to identify similar opinions through clustering, and then apply averaging, or any other aggregation function, over the cluster with the highest number of members to obtain the aggregated parameters that are closest to the ground truth. In other words, respect the majority as is done in democratic societies instead of averaging over all experts' parameters. The new approach is implemented and tested over several BNs with different numbers of variables and parameters, and with different numbers of experts. The results show that DemocraticOP outperforms two commonly used methods, LinOP and LogOP, in three key metrics: the average of absolute value of the difference between the true probability distribution and the one corresponding to the aggregated parameters, Kullback-Leibler divergence, and running time. (C) 2012 Elsevier Inc. All rights reserved.
bayesian networks aggregation function parameter aggregation