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- W4312866822 abstract "This paper elucidates the grouping effect of the sparse stable outlier-robust regression (S-SORR) estimator which exploits the minimax concave (MC) penalty and the Tikhonov regularization simultaneously together with the MC loss. The main theoretical result is the following: begin{equation*}Vert hat{x}_{i}vert -vert hat{x}_{j}Vert leqmu_{1}sqrt{2m(1-vert boldsymbol{a}_{i}^{top}boldsymbol{a}_{j}vert)},end{equation*} where <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$mu_{1} > 0$</tex> is the regularization parameter, and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$a_{i}$</tex> and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$a_{j}$</tex> are the unit vectors with their associated coefficients <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$hat{x}_{i}$</tex> and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$hat{x}_{j}$</tex> . Remarkably, the bound is independent of possible outliers which may be contained in the observation vector <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$y$</tex> , whereas the bound for the popular elastic net estimator increases in proportion to the norm of <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$y$</tex> which is largely affected by outliers. Numerical examples show that S-SORR extracts the group structure correctly under huge outliers." @default.
- W4312866822 created "2023-01-05" @default.
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- W4312866822 date "2022-08-22" @default.
- W4312866822 modified "2023-09-27" @default.
- W4312866822 title "On Grouping Effect of Sparse Stable Outlier-Robust Regression" @default.
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- W4312866822 doi "https://doi.org/10.1109/mlsp55214.2022.9943515" @default.
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