Addressing the Practical Limitations of Noisy-OR Using Conditional Inter-Causal Anti-Correlation with Ranked Nodes

Takao Noguchi,Martin Neil,Norman Fenton

doi:10.1109/tkde.2018.2873314

Takao Noguchi, Martin Neil + Show 1 more

Open Access

https://doi.org/10.1109/tkde.2018.2873314

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Abstract

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.

Highlights

BAYESIAN Networks (BNs) have been applied in many areas to provide practical solutions to risk assessment problems [1], [2]
The relationships between the variables are expressed as conditional probability tables
In the absence of relevant data a conditional probability table is typically elicited from human experts

Summary

INTRODUCTION

BAYESIAN Networks (BNs) have been applied in many areas to provide practical solutions to risk assessment problems [1], [2]. This can be a problem in practice since the underlying relationship often requires this explaining away behavior even when the effect is observed as false To see this consider again the above security breach example: if we know that a breach has not occurred, and discover that one of the most important types of threats has occurred, the probability that the remaining threats have occurred should clearly decrease. The ranked node solution directly and resolves another major limitation of the Noisy-OR function, namely that it is applicable only when all of the variables are binary This limitation has been addressed with various extensions to the NoisyOR function (typically to allow multiple-valued causes, for example noisy-MAX [8], [9]) these extensions retain the CII property of the Noisy-OR and still suffer from a lack of explaining away behavior when the effect is observed as false.

RANKED-NODE FUNCTION

CONDITIONAL ANTI-CORRELATION

IMPLICATIONS

CONCLUSION