Principal Component Regression Dominates all Monotone Spectral Filters for Linear Regression

arXiv:2609.39440 · stat.ML, cs.LG · Submitted 2026-09-30 · Read on arXiv

stat.ML, cs.LG

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Regularization — 35× in this paper · explained in 3 episodes
• Generalization — 4× in this paper · explained in 13 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Inverse Problem — 4× in this paper · explained in 2 episodes
• Gradient Flow — 3× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Admissibility — 1× in this paper · explained in 2 episodes
• Covariate Shift — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Scaling Laws — 1× in this paper · explained in 4 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes

Sources

• Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay
• De-floored Principal Component Regression: When Rank Selection Alone Is Insufficient for Prediction

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