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The Role of Regularization in Classification of High-dimensional Noisy Gaussian Mixture
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase regularization for convex losses with finite second derivative at the origin | Regularized convex classifiers · High-dimensional Gaussian mixture with equal cluster sizes (ρ = 0.5) | generalization error | Helped |
| Use the label-weighted sample average as the classifier and optimize its bias | Hebb plug-in estimator · High-dimensional Gaussian mixture | generalization error | Helped |
| Optimize regularization for square or logistic loss | Empirical risk minimization · High-dimensional Gaussian mixture with unequal cluster sizes (ρ ≠ 0.5) | generalization error | Mixed |
| Reduce regularization toward zero | Hinge and logistic classifiers · Linearly separable data (α < α*) | generalization error | No clear effect |
| Reduce regularization toward zero | Hinge and logistic classifiers · Non-separable data (α > α*) | generalization error | Mixed |
| Increase regularization | Square, hinge, and logistic classifiers · High-dimensional Gaussian mixture with equal cluster sizes | generalization error | Helped |
| Add regularization | Square, hinge, and logistic classifiers · High-dimensional Gaussian mixture | generalization error | Helped |
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