Research map / Learning theory and algorithms / Kernels and regression theory
No penalty no tears: Least squares in high-dimensional linear models
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RAT (ridge-based least-squares thresholding) instead of other methods for student grade prediction | RAT · Student performance (767 features) | mean error (RMSE): 1.90 vs 1.94 lasso, 1.92 scad/mc+ | Helped |
| Replace lasso with OLS-based screening plus thresholding and refinement (LAT) on the student dataset | LAT · Student performance excluding strong signals | mean error (RMSE): 4.50 vs 4.27 lasso | Hurt |
| Ridge-based least squares thresholding (RAT) on high-dimensional synthetic data with group structure | RAT · Synthetic (n,p)=(500,10000) Ex.(iii) | RMSE: 1.347 vs 7.326 lasso, 1.843 enet | Helped |
| Use OLS-based LAT instead of RAT on group structure | LAT · Synthetic (n,p)=(500,10000) Ex.(iii) | RMSE: 9.738 vs 1.347 for RAT | Hurt |
| Ridge adaptive thresholding (RAT) vs ordinary least squares variant (LAT) on independent, compound, factor synthetic designs (ablation) | RAT vs LAT · Synthetic (n,p)=(500,10000) Ex.(i),(ii),(iv) | RMSE: 0.263 vs 0.264; 0.204 vs 0.204; 0.168 vs 0.168 | No clear effect |
| Apply lasso followed by LAT/RAT stages (lasLAT/lasRAT) instead of plain lasso (ablation) | lasso · Synthetic (n,p)=(500,10000) Ex.(i) | RMSE: 0.214 lasLAT vs 0.781 lasso | Helped |
| Apply lasso followed by LAT/RAT stages (lasLAT) instead of plain lasso on compound symmetry (ablation) | lasso · Synthetic (n,p)=(500,10000) Ex.(ii) | RMSE: 0.260 lasLAT vs 0.979 lasso | Helped |
| Ridge stage (RAT) relative to OLS stage (LAT) on the student dataset with strong signals present (ablation) | RAT vs LAT · Student performance (767 features) | mean error (RMSE): 1.90 vs 1.93 | Helped |
| Ridge stage (RAT) relative to OLS stage (LAT) on the student dataset excluding strong signals (ablation) | RAT vs LAT · Student performance excluding strong signals | mean error (RMSE): 4.26 vs 4.50 | Helped |
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