Logistic Regression: From Art to Science
Logistic Regression: From Art to Science
复制标题
DOI：
10.1214/16-sts602
复制
发表时间：
2017-08-01
影响因子：
5.7
通讯作者：
King, Angela
中科院分区：
文献类型：
--
作者：
Bertsimas, Dimitris;King, Angela
高质量的逻辑回归模型包含各种理想的属性：预测能力，可解释性，显著性，对数据错误的鲁棒性和稀疏性等。为了实现这些相互竞争的目标，建模人员在最终模型上反复地合并这些属性。在1991年至2015年期间，混合线性优化（米洛）的算法进步加上硬件改进，导致在解决米洛问题方面的惊人的4500亿因子加速。出于这种加速的动机，我们提出了一个混合整数非线性优化（MINLO）的方法来建模逻辑回归问题的算法，以明确地将这些属性的联合，而不是顺序，时尚。由此产生的MINLO是灵活的，可以根据建模者的需求进行调整。使用真实的和合成数据，我们证明了整体方法是普遍适用的，并提供了高质量的解决方案，在现实的时间表，以及保证次优。当MINLO是不可行的，我们得到一个保证，强加不同的统计特性是根本不可行的。
A high quality logistic regression model contains various desirable properties: predictive power, interpretability, significance, robustness to error in data and sparsity, among others. To achieve these competing goals, modelers incorporate these properties iteratively as they hone in on a final model. In the period 1991-2015, algorithmic advances in Mixed-Integer Linear Optimization (MILO) coupled with hardware improvements have resulted in an astonishing 450 billion factor speedup in solving MILO problems. Motivated by this speedup, we propose modeling logistic regression problems algorithmically with a mixed integer nonlinear optimization (MINLO) approach in order to explicitly incorporate these properties in a joint, rather than sequential, fashion. The resulting MINLO is flexible and can be adjusted based on the needs of the modeler. Using both real and synthetic data, we demonstrate that the overall approach is generally applicable and provides high quality solutions in realistic timelines as well as a guarantee of suboptimality. When the MINLO is infeasible, we obtain a guarantee that imposing distinct statistical properties is simply not feasible.