论文标题
学习最佳分类树：强大的最大流程配方
Learning Optimal Classification Trees: Strong Max-Flow Formulations
论文作者
论文摘要
我们考虑学习最佳二进制分类树的问题。近年来，有关该主题的文献引起了人们的兴起，这是由于启发式方法的经验次优，以及混合企业编程（MIP）技术的巨大改进。但是，文献中现有的方法并不能完全利用MIP的力量。实际上，它们依靠弱制剂，从而导致缓慢的收敛性和较大的最佳差距。为了填补文献中的这一空白，我们提出了一种基于流动的MIP公式，用于最佳的二进制分类树，具有更强的线性编程松弛。我们的配方提出了一个有吸引力的分解结构。我们利用这种结构和最大流量/最小二元性来得出弯曲者的分解方法，该方法将其扩展到更大的实例。我们在标准基准数据集上进行了广泛的计算实验，我们表明我们的建议方法比基于MIP的最先进的技术快50倍，并提高了最高13.8％的样本性能。
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer programming (MIP) technology. Yet, existing approaches from the literature do not leverage the power of MIP to its full extent. Indeed, they rely on weak formulations, resulting in slow convergence and large optimality gaps. To fill this gap in the literature, we propose a flow-based MIP formulation for optimal binary classification trees that has a stronger linear programming relaxation. Our formulation presents an attractive decomposable structure. We exploit this structure and max-flow/min-cut duality to derive a Benders' decomposition method, which scales to larger instances. We conduct extensive computational experiments on standard benchmark datasets on which we show that our proposed approaches are 50 times faster than state-of-the art MIP-based techniques and improve out of sample performance up to 13.8%.
