Highly Adaptive Principal Component Regression

• URL: http://arxiv.org/abs/2602.10613v1
• Date: Wed, 11 Feb 2026 08:03:17 GMT
• Title: Highly Adaptive Principal Component Regression
• Authors: Mingxun Wang, Alejandro Schuler, Mark van der Laan, Carlos García Meixide,
• Abstract summary: We introduce the Principal Component based Highly Adaptive Lasso (PCHAL) and Principal Component based Highly Adaptive Ridge (PCHAR)<n>These estimators constitute an outcome-blind dimension reduction which offer substantial gains in computational efficiency.<n>We also uncover a striking spectral link between the leading principal components of the HAL/HAR Gram operator and a discrete sinusoidal basis.
• Score: 39.3660558859577
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 basis matrix it requires. The Highly Adaptive Ridge (HAR) has been proposed as a scalable alternative. Building on both procedures, we introduce the Principal Component based Highly Adaptive Lasso (PCHAL) and Principal Component based Highly Adaptive Ridge (PCHAR). These estimators constitute an outcome-blind dimension reduction which offer substantial gains in computational efficiency and match the empirical performances of HAL and HAR. We also uncover a striking spectral link between the leading principal components of the HAL/HAR Gram operator and a discrete sinusoidal basis, revealing an explicit Fourier-type structure underlying the PC truncation.

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