Boolean Decision Rules via Column Generation

TL;DR

This paper introduces a column generation approach for learning interpretable Boolean decision rules in DNF or CNF form, optimizing accuracy and simplicity without heuristic rule mining.

Contribution

It formulates an integer program for optimal rule learning and develops an efficient approximate column generation algorithm for large datasets.

Findings

Outperforms three recent methods on 7 out of 15 datasets.

Balances accuracy and simplicity effectively.

Finds simpler, accurate rules compared to existing approaches.

Abstract

This paper considers the learning of Boolean rules in either disjunctive normal form (DNF, OR-of-ANDs, equivalent to decision rule sets) or conjunctive normal form (CNF, AND-of-ORs) as an interpretable model for classification. An integer program is formulated to optimally trade classification accuracy for rule simplicity. Column generation (CG) is used to efficiently search over an exponential number of candidate clauses (conjunctions or disjunctions) without the need for heuristic rule mining. This approach also bounds the gap between the selected rule set and the best possible rule set on the training data. To handle large datasets, we propose an approximate CG algorithm using randomization. Compared to three recently proposed alternatives, the CG algorithm dominates the accuracy-simplicity trade-off in 7 out of 15 datasets. When maximized for accuracy, CG is competitive with rule learners designed for this purpose, sometimes finding significantly simpler solutions that are no less accurate.