Robust Grouped Variable Selection Using Distributionally Robust Optimization
نویسندگان
چکیده
We propose a distributionally robust optimization formulation with Wasserstein-based uncertainty set for selecting grouped variables under perturbations on the data both linear regression and classification problems. The resulting model offers robustness explanations least absolute shrinkage selection operator algorithms highlights connection between regularization. prove probabilistic bounds out-of-sample loss estimation bias, establish grouping effect of our estimator, showing that coefficients in same group converge to value as sample correlation covariates approaches 1. Based this result, we use spectral clustering algorithm Gaussian similarity function perform predictors, which makes approach applicable without knowing structure priori. compare an array alternatives provide extensive numerical results synthetic real large dataset surgery-related medical records, produces interpretable parsimonious encourages sparsity at level is able achieve better prediction performance presence outliers.
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ژورنال
عنوان ژورنال: Journal of Optimization Theory and Applications
سال: 2022
ISSN: ['0022-3239', '1573-2878']
DOI: https://doi.org/10.1007/s10957-022-02065-4