Rule generation for classification: Scalability, interpretability, and fairness

We introduce a new rule-based optimization method for classification with constraints. The proposed method leverages column generation for linear programming, and hence, is scalable to large datasets. The resulting pricing subproblem is shown to be NP-Hard. We recourse to a decision tree-based heuristic and solve a proxy pricing subproblem for acceleration. The method returns a set of rules along with their optimal weights indicating the importance of each rule for learning. We address interpretability and fairness by assigning cost coefficients to the rules and introducing additional constraints. In particular, we focus on local interpretability and generalize a separation criterion in fairness to multiple sensitive attributes and classes. We test the performance of the proposed methodology on a collection of datasets and present a case study to elaborate on its different aspects. The proposed rule-based learning method exhibits a good compromise between local interpretability and fairness on the one side, and accuracy on the other side. • Scalable algorithm using column generation for binary and multi-class classification. • Algorithm can incorporate additional constraints for group fairness definitions. • (Local) interpretability of the final rule set is considered in multiple ways. • Extensive experimental results show balance of accuracy, interpretability, fairness. • NP-hardness of pricing subproblem is proven and effective heuristic is proposed.