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An Extension to the Noisy-OR Function to Resolve the ‘Explaining Away’ Deficiency for Practical Bayesian Network Problems

The “leaky noisy-OR” function is a common and popular method used to simplify the elicitation of complex conditional probability tables in Bayesian networks involving Boolean variables. It has proven to be useful for approximating the required relationship in many real-world situations where there is a set of two or more variables that are potential causes of a single effect variable. However, one of the properties of leaky noisy-OR is Conditional Inter-causal Independence (CII). This property means that the ‘explaining away’ behavior—one of the most powerful benefits of BN inference—is not present when the effect variable is observed as false. Yet, for many real-world problems where the leaky noisy-OR has been considered, this behavior would be expected, meaning that leaky noisy-OR is deficient as an approximation of the required relationship in such cases. There have been previous attempts to adapt the noisy-OR to resolve this problem. However, they require too many additional parameters to be elicited. We describe a simple but powerful extension to leaky noisy-OR that requires only a single additional parameter. While it does not solve the CII problem in all cases, it does resolve most of the explaining away deficiencies that occur in practice. The problem and solution is illustrated using an example from intelligence analysis.