An Empirical Study of NIN-AND Tree Elicitation
Constructing a Bayesian Network requires the conditional probabilities table (CPT) to be acquired, one for each variable or node in the network. When data mining is not available, CPTs must be acquired from the domain experts. The complexity of the direct elicitation is exponential on the number of parents of a variable, making direct elicitation from human experts impractical for a large number of causes. Causal models such as Noisy-OR, Noisy-AND, Noisy-MIN, Noisy-MAX and Recursive Noisy-OR have been developed that allow CPTs acquisition to be achieved with linear complexity on the number of causes. Their representation power is measured by their ability to encode the causal interactions. Causal interactions can be categorized into two types: reinforcing and undermining. The Non-Impeding Noisy-AND or NIN-AND tree causal model, developed by Xiang and Jia, is capable of modeling both types of interaction while retaining the linear complexity. The main challenge in utilizing the NIN-AND tree model to generate a CPT is that it requires its tree topology to be elicited. A NIN-AND tree topology is an encoding of the causal interactions between the causes. In this work we present two methods, Structure Elimination (SE) and Pairwise Causal Interaction (PCI), that allow indirect elicitations of the NIN-AND tree topology using some additional probabilities elicited from experts. We conduct human-based experiment to investigate the e ectiveness of the two methods in terms of accuracy by comparing them to the Direct Numerical (DN) elicitation method. We recruit participants from second year Computer Science students at the University of Guelph. The process involves training a participant into domain expert using a known NIN-AND tree model then acquire another NIN-AND tree model by applying the SE and PCI methods. The CPTs produced by the acquired NIN-AND tree models are then compared to the one obtained by using the DN method. Comparable CPT accuracies are obtained among models generated by di erent methods, even though SE and PCI requires a much smaller number of parameters in comparison to DN.