Multi-objective Genetic Algorithm for Variable Selection in Linear Regression Model and Application
Dongil Kim, Cheong-Sool Park, Jun‐Geol Baek, Sung-Shick Kim · Journal of the Korea Society for Simulation · 2009
ABSTRACTThe purpose of this study is to implement variable selection algorithm which helps construct a reliable linear regression model. If we use all candidate variables to construct a linear regression model, the significance of the model will be decreased and it will cause 'Curse of Dimensionality'. And if the number of data is less than the number of variables (dimension), we cannot construct the regression model. Due to these problems, we consider the variable selection problem as a combinatorial optimization problem, and apply GA (Genetic Algorithm) to the problem. Typical measures of estimating statistical significance are , F-value of regression model, t-value of regression coefficients, and standard error of estimates. We design GA to solve multi-objective functions, because statistical significance of model is not to be estimated by a single measure. We perform experiments using simulation data, designed to consider various kinds of situations. As a result, it shows better performance than LARS (Least Angle Regression) which is an algorithm to solve variable selection problems. We modify algorithm to solve portfolio selection problem which construct portfolio by selecting stocks. We conclude that the algorithm is able to solve real problems.