Same-Decision Probability: threshold robustness and application to explanation

The same-decision probability (SDP) is a confidence measure for threshold-based decisions. In this paper we detail various properties of the SDP that allow for studying its robustness to changes in the threshold value upon which a decision is based. In addition to expressing confidence in a decision, the SDP has proven to be a useful tool in other contexts, such as that of information gathering. We demonstrate that the properties of the SDP as established in this paper allow for its application in the context of explaining Bayesian network classifiers as well.