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Non-asymptotic Analysis of Matérn Regression: The Roles of Target and Kernel Lengthscales — arXiv:2608.22553

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.22553
License (as archived): CC0-1.0
Archived: 2026-10-18T08:19:11.333Z
SHA-256 of the archived text: 47bd0d23418a0a9bfdc4d286d655bcd88bc587944fe01cdb27783c97b4d7c404
Stable URL of this page: https://metraipolis.com/documento/dc_fcffe4e785cf

How to cite

Non-asymptotic Analysis of Matérn Regression: The Roles of Target and Kernel Lengthscales — arXiv:2608.22553 — arXiv (en), https://arxiv.org/abs/2608.22553 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fcffe4e785cf (Metraipolis archive dc_fcffe4e785cf, sha256 47bd0d23418a0a9bfdc4d286d655bcd88bc587944fe01cdb27783c97b4d7c404)

BibTeX

@misc{dcfcffe4e785cf,
  title = {Non-asymptotic Analysis of Matérn Regression: The Roles of Target and Kernel Lengthscales — arXiv:2608.22553},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.22553},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fcffe4e785cf; sha256 47bd0d23418a0a9bfdc4d286d655bcd88bc587944fe01cdb27783c97b4d7c404},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.22553. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Theoretical guarantees for kernel regression are typically formulated in terms of smoothness, but practical accuracy depends critically on how the design resolution compares with the target and kernel lengthscales. We develop a finite-sample theory for Matérn regression on periodic domains with quasi-uniform designs, covering noiseless interpolation and noisy kernel ridge regression. Our minimax result shows that accurate recovery requires a design dense enough to resolve the target lengthscale and sufficient information at that scale to overcome noise. We prove that Matérn interpolation additionally requires the design to resolve the kernel lengthscale: if the kernel is too short relative to the point spacing, an additional error remains even when the target is well resolved. For noisy Matérn regression, we derive a three-term fixed-ridge risk characterization consisting of target-scale bias, kernel-scale bias, and variance, and show that optimizing over the ridge parameter yields four distinct contributions. When the target is no more than twice as smooth as the kernel, choosing a kernel lengthscale longer than the target does not worsen the oracle risk, whereas choosing one too short can. Thus these resolution conditions determine when accurate recovery becomes possible, while smoothness determines how rapidly the error decreases thereafter.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-25 in stat.CO).
Categorie arXiv: Statistics Theory (math.ST) ; Numerical Analysis (math.NA); Computation (stat.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.22553 — 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 2026-10-18T08:17:34.685Z dalla pagina https://arxiv.org/catchup/stat.CO/2026-08-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).