Research map / Learning theory and algorithms / Matrix and tensor methods
A Comparison of Hamming Errors of Representative Variable Selection Methods
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add coordinate-wise hard thresholding after Lasso (ablation) | Lasso · Block-diagonal and general designs | expected Hamming error: 35.62 (5.09) -> 15.62 (4.06); 47.15 (6.32) -> 22.02 (5.31); 21.14 (4.52) -> 15.90 (3.87) | Helped |
| Add coordinate-wise hard thresholding after Lasso (ablation) | Lasso · Random design, p>n | expected Hamming error: 16.02 (5.52) -> 9.83 (4.08); 18.49 (6.03) -> 10.50 (4.23) | Helped |
| Replace the L1 penalty with SCAD | Lasso · Block-diagonal design with negative correlation | upper phase curve for exact recovery | Helped |
| Replace the L1 penalty with SCAD | Lasso · Block-diagonal design with nonnegative correlation | upper phase curve for exact recovery | No clear effect |
| Add an L2 penalty to the L1 objective | Lasso · Block-wise diagonal design | upper phase curve for exact recovery | Hurt |
| Add a backward thresholding step after forward selection (ablation) | Forward selection · Block-wise diagonal design | upper phase curve for exact recovery | Helped |
| Add a backward thresholding step after forward selection (ablation) | Forward selection · Toeplitz design | expected Hamming error: 30.77 (6.18) -> 22.93 (5.44) | Helped |
| Add a backward thresholding step after forward selection (ablation) | Forward selection · Factor model design | expected Hamming error: 20.04 (4.34) -> 16.13 (3.76) | Helped |
| Add a backward thresholding step after forward selection (ablation) | Forward selection · Random design, p>n | expected Hamming error: 11.74 (5.55) -> 9.84 (4.93); 12.00 (5.67) -> 10.41 (5.03) | Helped |
| Use thresholded Lasso instead of SCAD | SCAD · Block-diagonal design with negative correlation | expected Hamming error: 25.87 (5.04) -> 15.62 (4.06) | Helped |
| Use thresholded Lasso instead of Elastic net | Elastic net · Toeplitz design | expected Hamming error: 47.40 (6.41) -> 22.02 (5.31) | Helped |
| Tune both the Lasso penalty and the post-Lasso threshold (ablation) | Lasso · Block-wise diagonal design | expected Hamming error | Helped |
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