A new method to compare the interpretability of rule-based algorithms

Interpretability is becoming increasingly important for predictive model analysis. Unfortunately, as remarked by many authors, there is still no consensus regarding this notion. The goal of this article is to propose a definition of the notion of interpretability that allows comparisons of rule-based algorithms. This definition consists of three terms, each one being quantitatively measured with a simple formula: predictivity, stability and simplicity. While predictivity has been extensively studied to measure the accuracy of predictive algorithms, stability is based on the Dice-Sorensen index for comparing two sets of rules generated by an algorithm using two independent samples. The simplicity is based on the sum of the length of the rules derived from the predictive model. The new measure for the interpretability of a rule-based algorithm is a weighted sum of the three terms mentioned above. We use the new measure to compare the interpretability of several rule-based algorithms, specifically CART, RuleFit, Node Harvest, Covering algorithm and SIRUS for the regression case, and CART, PART and RIPPER for the classification case