Research map / Learning theory and algorithms / Matrix and tensor methods
Generalized Linear Model Regression under Distance-to-set Penalties
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use distance penalties with MM instead of shrinkage penalties | Sparse Poisson and logistic regression · Synthetic sparse regression | mean squared error | Helped |
| Use distance penalties with MM instead of LASSO | Sparse Poisson and logistic regression · Synthetic sparse regression | relative error | Helped |
| Use rank-set projections instead of spectral shrinkage | Matrix regression · Synthetic cross-shaped rank-2 signal | signal recovery | Helped |
| Use distance-penalized MM | EEG alcoholism regression · EEG alcoholism | misclassification error: 0.1475 vs 0.139 | Mixed |
| Use distance-penalized MM rather than relaxed LASSO | Gaussian linear regression · Gaussian regression simulation | MSE | No clear effect |
| Use distance-penalized MM rather than relaxed LASSO | Gaussian linear regression · Gaussian regression simulation | average total runtime: 96.8 vs 4876.6 seconds | Helped |
| Account for matrix structure with a rank constraint rather than sparsity alone (ablation) | Distance-penalized matrix regression · Synthetic cross-shaped rank-2 signal | signal recovery | Helped |
| Set the rank constraint to 2 (ablation) | Distance-penalized matrix regression · Synthetic cross-shaped rank-2 signal | signal recovery | Helped |
| Vary the rank constraint from 1 to 8 (ablation) | Distance-penalized matrix regression · Synthetic cross-shaped rank-2 signal | signal recovery | No clear effect |
| Use an ℓ1 penalty instead of a rank constraint (ablation) | EEG alcoholism regression · EEG alcoholism | useful signal recovery | Hurt |
| Use nuclear-norm shrinkage instead of rank-set distance penalization (ablation) | EEG alcoholism regression · EEG alcoholism | low-rank solution | Hurt |
| Use rank restriction rather than sparsity restriction (ablation) | Matrix regression · Synthetic cross-shaped rank-2 signal | signal recovery | Helped |
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