  Interpretability is having an increasingly important role in the design of
machine learning algorithms. However, interpretable methods tend to be less
accurate than their black-box counterparts. Among others, DNFs (Disjunctive
Normal Forms) are arguably the most interpretable way to express a set of
rules. In this paper, we propose an effective bottom-up extension of the
popular FIND-S algorithm to learn DNF-type rulesets. The algorithm greedily
finds a partition of the positive examples. The produced DNF is a set of
conjunctive rules, each corresponding to the most specific rule consistent with
a part of positive and all negative examples. We also propose two principled
extensions of this method, approximating the Bayes Optimal Classifier by
aggregating DNF decision rules. Finally, we provide a methodology to
significantly improve the explainability of the learned rules while retaining
their generalization capabilities. An extensive comparison with
state-of-the-art symbolic and statistical methods on several benchmark data
sets shows that our proposal provides an excellent balance between
explainability and accuracy.

Machine Learning