Addressing the Practical Limitations of Noisy-OR Using Conditional Inter-Causal Anti-Correlation with Ranked Nodes
Takao Noguchi, Norman Fenton, Martin Neil · IEEE Transactions on Knowledge and Data Engineering · 2018
Numerous methods have been proposed to simplify the problem of eliciting complex conditional probability tables in Bayesian networks. One of the most popular methods -“Noisy-OR”- approximates the required relationship in many real-world situations between a set of variables that are potential causes of an effect variable. However, the Noisy-OR function has the conditional inter-causal independence (CII) property which means that `explaining away' behavior-one of the most powerful benefits of BN inference-is not present when the effect variable is observed as false. Hence, for many real-world problems where the Noisy-OR has been used or proposed, it may be deficient as an approximation of the required relationship. However, there is a very simple alternative solution, namely to define the variables as ranked nodes and to use the ranked node weighted average function. This does not have the CII property-instead, we prove it has the conditional anti-correlation property required to ensure that explaining away works in all cases. Moreover, ranked node variables are not restricted to binary states, and hence provide a more comprehensive and general solution to Noisy-OR in all cases.