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 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.

翻译：我们提出了一种用于带约束分类的新型基于规则的优化方法。所提方法利用线性规划的列生成技术，因此可扩展至大规模数据集。结果表明，所衍生的定价子问题为NP难问题。我们借助基于决策树的启发式方法，通过求解代理定价子问题实现加速。该方法返回一组规则及其最优权重，权重体现了每条规则在学习中的重要性。我们通过为规则分配成本系数并引入额外约束来处理可解释性与公平性，尤其关注局部可解释性，并将公平性中的分离准则推广至多敏感属性与多类别场景。我们在一组数据集上测试了所提方法的性能，并通过案例研究阐述其不同特性。该基于规则的分类方法在局部可解释性与公平性、以及准确性之间展现了良好的平衡。