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The problem of parameters determination of a linear regression model with the least moduli criterion powered to \(1\le p\le 2\) with \({L}_{1}\) -regularization is investigated. It corresponds to the problem of unconditional minimization of a non-smooth convex piecewise linear function. The formulation of the problem with \(p=1\) and the linear programming problem corresponding to it are given. For determination of model parameters, the emlmpr algorithm is proposed, which implements the Shor’s ellipsoid method. The Octave-code of the algorithm and the results of three computational experiments are given. The first experiment is designed to estimate the amount of time needed to solve the problem. The purpose of the second experiment is to demonstrate the robustness of the least moduli method. The third experiment is designed to investigate the effect of \({L}_{1}\) -regularization on parameters determination of a model, in which there are linear relationships between factors. The effect of the regularization parameter value on the quality of the model parameters determination with different coefficients for dependent factors is analyzed.

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Using of Ellipsoid Method for Finding Linear Regression Parameters with L1-Regularization

  • 会议论文

  • 发表日期：

    2025年

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  • Petro Stetsyuk,
  • Viktor Stovba,
  • Mykola Korablov

摘要

The problem of parameters determination of a linear regression model with the least moduli criterion powered to \(1\le p\le 2\) with \({L}_{1}\) -regularization is investigated. It corresponds to the problem of unconditional minimization of a non-smooth convex piecewise linear function. The formulation of the problem with \(p=1\) and the linear programming problem corresponding to it are given. For determination of model parameters, the emlmpr algorithm is proposed, which implements the Shor’s ellipsoid method. The Octave-code of the algorithm and the results of three computational experiments are given. The first experiment is designed to estimate the amount of time needed to solve the problem. The purpose of the second experiment is to demonstrate the robustness of the least moduli method. The third experiment is designed to investigate the effect of \({L}_{1}\) -regularization on parameters determination of a model, in which there are linear relationships between factors. The effect of the regularization parameter value on the quality of the model parameters determination with different coefficients for dependent factors is analyzed.