用混合非线性规划极小化线性回归分析中的Akaike信息准则
Minimization of Akaike's Information Criterion in Linear Regression Analysis via Mixed Integer Nonlinear Program
摘要：
赤池信息准则（Akaike's Information Criterion，AIC）是一种衡量给定数据集的统计模型质量的标准。我们可以通过AIC的最小化来确定特定数据集的最佳统计模型。由于我们需要通过AIC的最小化来指数地评估模型的许多候选者，因此最小化是不合理的。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。我们提出了一个分支定界搜索算法，用于Miyashiro和Takano（2015）的AIC最小化的混合整数非线性规划公式。更具体地说，我们提出的方法来找到下限和上界，和分支规则，这个最小化。然后，我们将它们与SCIP相结合，SCIP是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统计模型的基础上AIC的小型或中型的基准数据集在UCI机器学习知识库。此外，我们表明，这种方法找到了高质量的解决方案，为大型基准数据集。
英文摘要：
Akaike's information criterion (AIC) is a measure of the quality of a statistical model for a given set of data. We can determine the best statistical model for a particular data set by the minimization of the AIC. Since we need to evaluate exponentially many candidates of the model by the minimization of the AIC, the minimization is unreasonable. Instead, stepwise methods, which are local search algorithms, are commonly used to find a better statistical model though it may not be the best. We propose a branch and bound search algorithm for a mixed integer nonlinear programming formulation of the AIC minimization by Miyashiro and Takano (2015). More concretely, we propose methods to find lower and upper bounds, and branching rules for this minimization. We then combine them with SCIP, which is a mathematical optimization software and a branch-and-bound framework. We show that the proposed method can provide the best statistical model based on AIC for small-sized or medium-sized benchmark data sets in UCI Machine Learning Repository. Furthermore, we show that this method finds good quality solutions for large-sized benchmark data sets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
