Highly Adaptive Ridge

• URL: http://arxiv.org/abs/2410.02680v1
• Date: Thu, 3 Oct 2024 17:06:06 GMT
• Title: Highly Adaptive Ridge
• Authors: Alejandro Schuler, Alexander Hagemeister, Mark van der Laan,
• Abstract summary: We propose a regression method that achieves a $n-2/3$ dimension-free L2 convergence rate in the class of right-continuous functions with square-integrable sectional derivatives. Har is exactly kernel ridge regression with a specific data-adaptive kernel based on a saturated zero-order tensor-product spline basis expansion. We demonstrate empirical performance better than state-of-the-art algorithms for small datasets in particular.
• Score: 84.38107748875144
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we propose the Highly Adaptive Ridge (HAR): a regression method that achieves a $n^{-1/3}$ dimension-free L2 convergence rate 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. HAR is exactly kernel ridge regression with a specific data-adaptive kernel based on a saturated zero-order tensor-product spline basis expansion. We use simulation and real data to confirm our theory. We demonstrate empirical performance better than state-of-the-art algorithms for small datasets in particular.

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