Explaining Naive Bayes and Other Linear Classifiers with Polynomial Time and Delay

Recent work proposed the computation of so-called PIexplanations of Naive Bayes Classifiers (NBCs) [29]. PIexplanations are subset-minimal sets of feature-value pairs that are sufficient for the prediction, and have been computed with state-of-the-art exact algorithms that are worst-case exponential in time and space. In contrast, we show that the computation of one PIexplanation for an NBC can be achieved in log-linear time, and that the same result also applies to the more general class of linear classifiers. Furthermore, we show that the enumeration of PIexplanations can be obtained with polynomial delay. Experimental results demonstrate the performance gains of the new algorithms when compared with earlier work. The experimental results also investigate ways to measure the quality of heuristic explanations.