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Principal Component Regression Dominates all Monotone Spectral Filters for Linear Regression — arXiv:2609.39440

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.39440
License (as archived): CC0-1.0
Archived: 2026-10-07T13:47:37.111Z
SHA-256 of the archived text: 45b0af56769ab93f7b25311ecceaaa2e1c1c765ddae0ba4ed47e25d3f0446c68
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How to cite

Principal Component Regression Dominates all Monotone Spectral Filters for Linear Regression — arXiv:2609.39440 — arXiv (en), https://arxiv.org/abs/2609.39440 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_acc024658a3e (Metraipolis archive dc_acc024658a3e, sha256 45b0af56769ab93f7b25311ecceaaa2e1c1c765ddae0ba4ed47e25d3f0446c68)

BibTeX

@misc{dcacc024658a3e,
  title = {Principal Component Regression Dominates all Monotone Spectral Filters for Linear Regression — arXiv:2609.39440},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.39440},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_acc024658a3e; sha256 45b0af56769ab93f7b25311ecceaaa2e1c1c765ddae0ba4ed47e25d3f0446c68},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.39440. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We compare the instance-wise, finite-sample risks of monotone spectral filters for linear regression, a broad class of estimators including principal component regression (PCR), gradient descent (GD), and ridge regression. We show that PCR dominates all monotone spectral filters: compared to any such filter, the risk of optimally tuned PCR is no bigger by a constant factor for all problems. Furthermore, the dominance is strong if the filter is separated from step functions (e.g., GD and ridge): there exist problem instances for which the risk of PCR is smaller by a polynomial factor in sample size dependence. Our comparison results show that PCR is optimal and thus admissible among monotone filters, significantly extending Wu et al. (2026)'s result that GD strongly dominates ridge. From a technical perspective, we establish new upper and lower bounds for general spectral filters, which are instance-wise sharp when specialized to ridge or GD, recovering or improving the best-known bounds.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-10-01 in cs.LG).
Categorie arXiv: Machine Learning (stat.ML) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.39440 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T13:18:10.646Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).