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.

翻译：本文提出高度自适应岭回归（HAR）：一种回归方法，在具有平方可积截面导数的右连续函数类中，实现了维度无关的$n^{-1/3}$ L2收敛速率。这是一个适用于表格数据的非参数函数大类。HAR本质上是基于特定数据自适应核的核岭回归，该核建立在饱和零阶张量积样条基展开之上。我们通过仿真和真实数据验证了理论，并证明该方法在小数据集上的经验性能优于现有先进算法。