Principal Component Regression Dominates all Monotone Spectral Filters for Linear Regression
We compare the instance-wise, finite-sample risks of monotone spectral filters for linear regression, a broad class of estimators including principal component regression (PCR), gradient descent (GD), and ridge regression. We show that PCR dominates all monotone spectral filters: compared to any such filter, the risk of optimally tuned PCR is no bigger by a constant factor for all problems. Furthermore, the dominance is strong if the filter is separated from step functions (e.g., GD and ridge): there exist problem instances for which the risk of PCR is smaller by a polynomial factor in sample size dependence. Our comparison results show that PCR is optimal and thus admissible among monoto...
| Authors | Juno Kim, Hengyu Fu, Peter Bartlett et al. |
|---|---|
| Primary category | stat.ML |
| Published | 30 September 2026 |
| Last updated at source | 30 September 2026 |
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