The article introduces KORE, a method that determines optimal spline regression resolution in closed form rather than through exhaustive hyperparameter search. By leveraging classical approximation theory and the PRESS identity, it analytically balances bias and noise scales to achieve accuracy comparable to grid sweeps with significantly less compute.
- KORE replaces ambient input dimension with interaction order, creating a scaling law where optimal resolution is a power function of effective density.
- The algorithm fits two pilot resolutions and solves a leverage-calibrated 2x2 system to estimate bias and noise scales for a closed-form plug-in resolution.
- It requires only about a dozen model fits compared to a full grid sweep, offering a consistency guarantee as sample size grows.
- On 36 real tabular datasets up to 80 dimensions, KORE ranks first among 21 methods in accuracy per unit of compute, outperforming tuned boosters and kernel machines.
This approach allows spline regression to bypass the computational cost of hyperparameter tuning while maintaining high predictive performance on low interaction order targets.