Highly Adaptive Principal Component Regression
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917460035239936 |
|---|---|
| author | Wang, Mingxun Schuler, Alejandro van der Laan, Mark Meixide, Carlos García |
| author_facet | Wang, Mingxun Schuler, Alejandro van der Laan, Mark Meixide, Carlos García |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10613 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Highly Adaptive Principal Component Regression Wang, Mingxun Schuler, Alejandro van der Laan, Mark Meixide, Carlos García Machine Learning 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. |
| title | Highly Adaptive Principal Component Regression |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.10613 |