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Sparse regression for large data sets with outliers

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  • Bottmer, Lea
  • Croux, Christophe
  • Wilms, Ines

Abstract

The linear regression model remains an important workhorse for data scientists. However, many data sets contain many more predictors than observations. Besides, outliers, or anomalies, frequently occur. This paper proposes an algorithm for regression analysis that addresses these features typical for big data sets, which we call “sparse shooting S”. The resulting regression coefficients are sparse, meaning that many of them are set to zero, hereby selecting the most relevant predictors. A distinct feature of the method is its robustness with respect to outliers in the cells of the data matrix. The excellent performance of this robust variable selection and prediction method is shown in a simulation study. A real data application on car fuel consumption demonstrates its usefulness.

Suggested Citation

  • Bottmer, Lea & Croux, Christophe & Wilms, Ines, 2022. "Sparse regression for large data sets with outliers," European Journal of Operational Research, Elsevier, vol. 297(2), pages 782-794.
    • Handle: RePEc:eee:ejores:v:297:y:2022:i:2:p:782-794
    DOI: 10.1016/j.ejor.2021.05.049
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    5. Su, Peng & Tarr, Garth & Muller, Samuel & Wang, Suojin, 2024. "CR-Lasso: Robust cellwise regularized sparse regression," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).

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