# Highly Adaptive Ridge

arXiv: https://arxiv.org/abs/2410.02680 · HTML: https://mlsanity.com/paper/2410.02680/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 34 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## Builds on (most cited first, 5 of 5)

- [Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review](https://mlsanity.com/paper/1611.00740/) (2016)
- [Multivariate extensions of isotonic regression and total variation denoising via entire monotonicity and Hardy-Krause variation](https://mlsanity.com/paper/1903.01395/) (2019)
- [Nonlinear functional regression by functional deep neural network with kernel embedding](https://mlsanity.com/paper/2401.02890/) (2024)
- [Lassoed Tree Boosting](https://mlsanity.com/paper/2205.10697/) (2022)
- [Regression in Tensor Product Spaces by the Method of Sieves](https://mlsanity.com/paper/2206.02994/) (2022)

## Built on by (most cited first, 2 of 2)

- [Highly Adaptive Principal Component Regression](https://mlsanity.com/paper/2602.10613/) (2026)
- [Seeing the Forest for the Trees: The Gaussian Process Limit of BART](https://mlsanity.com/paper/2607.28844/) (2026)

## Abstract (arXiv)

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.