Minimization of Akaike's information criterion in linear regression analysis via mixed integer nonlinear program
Minimization of Akaike's information criterion in linear regression analysis via mixed integer nonlinear program
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DOI：
10.1080/10556788.2017.1333611
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发表时间：
2018-01-01
影响因子：
2.2
通讯作者：
Waki, Hayato
中科院分区：
文献类型：
--
作者：
Kimura, Keiji;Waki, Hayato
赤池信息准则（Akaike's information criterion，AIC）是一种对给定数据集的统计模型进行评估的方法。我们可以通过找到具有最小AIC值的模型来确定特定数据集的最佳统计模型。由于最佳模型的候选者呈指数级地多，因此计算所有模型的AIC值是不切实际的。相反，逐步方法，这是局部搜索算法，通常用于找到一个更好的统计模型，虽然它可能不是最好的模型。我们提出了一个分支定界搜索算法的混合整数非线性规划公式的AIC最小化提出的宫和高野[混合整数二阶锥规划公式变量选择，欧洲。J. Oper。247（2015），pp. 721-731]。更具体地说，我们提出了程序，以找到下限和上限，并分支规则，这种最小化。然后，我们结合联合收割机这样的程序和分支规则与SCIP，一个数学优化软件和分支定界框架。我们表明，所提出的方法可以提供最好的基于AIC的统计模型的小型或中型的基准数据集在UCI机器学习存储库。此外，该方法发现高质量的解决方案，为大型基准数据集。
Akaike's information criterion (AIC) is a measure of evaluating statistical models for a given data set. We can determine the best statistical model for a particular data set by finding the model with the smallest AIC value. Since there are exponentially many candidates of the best model, the computation of the AIC values for all the models is impractical. Instead, stepwise methods, which are local search algorithms, are commonly used to find a better statistical model, though it may not be the best model. We propose a branch-and-bound search algorithm for a mixed integer nonlinear programming formulation of the AIC minimization presented by Miyashiro and Takano [Mixed integer second-order cone programming formulations for variable selection, Eur. J. Oper. Res. 247 (2015), pp. 721-731]. More concretely, we propose procedures to find lower and upper bounds, and branching rules for this minimization. We then combine such procedures and branching rules with SCIP, a mathematical optimization software and the branch-and-bound framework. We show that the proposed method can provide the best AIC-based statistical model for small- or medium-sized benchmark data sets in the UCI Machine Learning Repository. Furthermore, the proposed method finds high-quality solutions for large-sized benchmark data sets.