In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction. Despite comprehensive efforts on learning monotonic classifiers, dedicated approaches for explaining monotonic classifiers are scarce and classifier-specific. This paper describes novel algorithms for the computation of one formal explanation of a (black-box) monotonic classifier. These novel algorithms are polynomial (indeed linear) in the run time complexity of the classifier. Furthermore, the paper presents a practically efficient model-agnostic algorithm for enumerating formal explanations.

Recent work proposed the computation of so-called PI-explanations of Naive Bayes Classifiers (NBCs). PI-explanations 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 PI-explanation 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 PI-explanations 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.