Research map / Learning theory and algorithms / Kernels and regression theory
A theory of high dimensional regression with arbitrary correlations between input features and target functions: sample complexity, multiple descent curves and a hierarchy of phase transitions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| isotropic input covariance instead of anisotropic (aspect ratio 1) for a random (unaligned) target | ridge regression with random target function · two-scale model, theory and simulation | fraction of unexplained variance F | Helped |
| aligning the target weights with high-variance data directions at fixed SNR | ridge regression with optimal lambda · two-scale model, aspect ratio 10 | sample complexity to reach fixed error F | Helped |
| optimal regularization instead of fixed small lambda (lambda optimized per alpha) (ablation) | ridge regression, two-scale model S1=1, S2=10^-2 · multiple descent learning curves | test error vs alpha (peaks at alpha=1/2 and 1) | Helped |
| increasing number of scales (three-scale model) with low lambda | ridge regression with multi-scale covariance · three-scale model scales 10^-1,10^-3,10^-5 | error peaks vs alpha | No clear effect |
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