Comparing quantified MAP-dependence to other measures of relevance in Bayesian networks

Abstract

In the fields of explainable AI and Bayesian networks, a recently introduced concept is a measure called MAP-independence. It is meant to assist in the justification of decisions made using decision support systems, by identifying irrelevant intermediate variables in a decision problem. In this paper, we argue that the binary nature of this measure is too crude, and may lead to a large set of relevant variables, some of which only change the Maximum A Posteriori outcome for very specific and maybe unlikely observations. We hypothesise that “quantifying” the measure (meaning “to change it from a binary measure to a measure on the [0,1] scale”) would allow us to identify differences in how relevant each variable in a set of relevant variables is. We name this new measure quantified MAP-dependence. We make an implementation which is, to the best of our knowledge, the first implementation of both MAP-independence and quantified MAP-dependence. Furthermore, we apply these measures to the ALARM network. For comparison, we also apply an older measure of relevance named intrinsic relevance. Based on the results, we conclude the following: Firstly, that our hypothesis about the usefulness of quantifying MAP-independence is true. Secondly, that compared to intrinsic relevance, quantified MAP-dependence describes a fundamentally different interpretation of what makes an intermediate variable relevant.