# Highly Adaptive Principal Component Regression

arXiv: https://arxiv.org/abs/2602.10613 · HTML: https://mlsanity.com/paper/2602.10613/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 56 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Builds on (most cited first, 3 of 3)

- [Adaptive piecewise polynomial estimation via trend filtering](https://mlsanity.com/paper/1304.2986/) (2013)
- [Multivariate extensions of isotonic regression and total variation denoising via entire monotonicity and Hardy-Krause variation](https://mlsanity.com/paper/1903.01395/) (2019)
- [Highly Adaptive Ridge](https://mlsanity.com/paper/2410.02680/) (2024)

## Built on by (most cited first, 1 of 1)

- [Improving the Efficiency of Subgroup Analysis in Randomized Controlled Trials with TMLE](https://mlsanity.com/paper/2605.15483/) (2026)

## Abstract (arXiv)

The Highly Adaptive Lasso (HAL) is a nonparametric regression method that achieves almost dimension-free convergence rates under minimal smoothness assumptions, but its implementation can be computationally prohibitive in high dimensions due to the large design matrix it requires. The Highly Adaptive Ridge (HAR) has been proposed as a related ridge-regularized analogue. Building on both procedures, we introduce the Principal Component Highly Adaptive Lasso (PCHAL) and Principal Component Highly Adaptive Ridge (PCHAR). These estimators use an outcome-blind principal-component reduction of the HAL basis, offering substantial computational gains over HAL while achieving empirical performance comparable to HAL and HAR. We also describe an early-stopped gradient descent variant, which provides a convenient form of smooth spectral regularization without explicitly selecting a hard principal-component cutoff. Finally, we uncover that under special circumstances, the HAL kernel is identical to the covariance function of Brownian motion.