analiza aiqbench
This paper proposes a nonparametric regression method whose error rate doesn't depend on the number of features, and it shows that for squared error the method is exactly kernel ridge regression with a data-adaptive kernel. That equivalence makes it easier to analyze and compute than its novelty suggests, and it links the approach to established Sobolev-space theory. For tabular-data practitioners, the main question is whether the theoretical rate translates into gains over standard kernel methods and gradient-boosted trees on real datasets, which the authors test only with simulations and limited real data.
Highly Adaptive Ridge
arXiv:2410.02680v2 Announce Type: replace-cross Abstract: In this paper we propose the Highly Adaptive Ridge (HAR): a regression method that achieves an $n^{-1/3}$ dimension-free $\mathscr L_2$ convergence rate (up to log factors) in the class of right-continuous functions with square-integrable sectional derivatives. This is a large nonparametric function class that is particularly appropriate for tabular data. For squared error loss, HAR is exactly kernel ridge regression with a specific data-adaptive kernel based on a saturated zero-order tensor-product spline basis expansion, and thus scales reasonably well, computationally. We prove close connections between HAR and kernel ridge regression in Sobolev spaces of dominating mixed derivatives, and highlight practical differences. We use simulation and real data to confirm our theory.
Abstract:In this paper we propose the Highly Adaptive Ridge (HAR): a regression method that achieves an $n^{-1/3}$ dimension-free $\mathscr L_2$ convergence rate (up to log factors) in the class of right-continuous functions with square-integrable sectional derivatives. This is a large nonparametric function class that is particularly appropriate for tabular data. For squared error loss, HAR is exactly kernel ridge regression with a specific data-adaptive kernel based on a saturated zero-order tensor-product spline basis expansion, and thus scales reasonably well, computationally. We prove close connections between HAR and kernel ridge regression in Sobolev spaces of dominating mixed derivatives, and highlight practical differences. We use simulation and real data to confirm our theory.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2410.02680 [stat.ML]
(or arXiv:2410.02680v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2410.02680 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 206 cuvinte
Subiecte conexe
Neural Barriers: An Online Certifiable Learning-enhanced Adaptive High Order Safety Critical Control
arXiv · 6 oct. 2026
Forensics Adapter: Unleashing CLIP for Generalizable Face Forgery Detection
arXiv · 27 iul. 2026
Noise-Adaptive High-Probability Regret Bounds for Online Convex Optimization
arXiv · 9 iun. 2026
A Morphing Aerial Robot With Thruster-Integrated Flexible Continuum Links for Shape Adaptive Aerial Manipulation
arXiv · 18 sept. 2026