Best Subset Selection for Linear Regression Models via Mixed-Integer Optimization

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  • 混合整数最適化による線形回帰モデルの最良変数選択
  • コンゴウ セイスウ サイテキカ ニ ヨル センケイ カイキ モデル ノ サイリョウ ヘンスウ センタク

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<p>Subset selection for regression models has long been recognized as an important task in statistics, and recently it has been actively studied in data mining and machine learning because of the increased amount of data handled. A mixed-integer optimization approach, which has received renewed attention for subset selection, is to formulate subset selection as a mathematical optimization problem and to solve it using a branch-and-bound method. The greatest advantage of this approach is that the best subset of explanatory variables can be selected with respect to the objective function (i.e., evaluation criteria of regression models) of the optimization problem. The authors have devised several formulations for simultaneously optimizing a subset of variables and its cardinality in terms of statistical criteria such as Mallows' Cp, adjusted R2, information criteria, and cross-validation criterion. In this paper, we explain these mixed-integer optimization formulations for best subset selection in linear regression models.</p>

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