A Local-branching Heuristic for the Best Subset Selection Problem in Linear Regression

T. Bigler, O. Strub
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Abstract

The best subset selection problem in linear regression consists of selecting a small subset with a given maximum cardinality of a set of features, i.e explanatory variables, to build a linear regression model that is able to explain a given set of observations of a response variable as exactly as possible. The motivation in building linear regression models that include only a small number of features is that these models are easier to interpret. In this paper, we present a heuristic based on the concept of local branching. Such a heuristic repeatedly performs local-search iterations by applying mixed-integer programming. In each local-search iteration, we consider a different randomly selected subset of the features to reduce the required computational time. The results of our computational tests demonstrate that the proposed local-branching heuristic delivers better linear regression models than a pure mixed-integer programming approach within a limited amount of computational time.
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线性回归中最优子集选择问题的局部分支启发式
线性回归中的最佳子集选择问题包括选择具有一组特征(即解释变量)的给定最大基数的小子集,以构建能够尽可能准确地解释响应变量的给定观察集的线性回归模型。建立只包含少量特征的线性回归模型的动机是这些模型更容易解释。本文提出了一种基于局部分支概念的启发式算法。这种启发式算法通过混合整数规划重复执行局部搜索迭代。在每次局部搜索迭代中,我们考虑不同的随机选择的特征子集,以减少所需的计算时间。我们的计算测试结果表明,在有限的计算时间内,所提出的局部分支启发式方法比纯混合整数规划方法提供了更好的线性回归模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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