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Large deviations for linear regressions — arXiv:2609.03111

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.03111
License (as archived): CC0-1.0
Archived: 2026-10-17T03:07:15.465Z
SHA-256 of the archived text: 2b43b4e24753b1498b2f4fae9dd48dd1429d0025d926ae1f2e35bbb110bf6ee4
Stable URL of this page: https://metraipolis.com/documento/dc_495c53a48d66

How to cite

Large deviations for linear regressions — arXiv:2609.03111 — arXiv (en), https://arxiv.org/abs/2609.03111 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_495c53a48d66 (Metraipolis archive dc_495c53a48d66, sha256 2b43b4e24753b1498b2f4fae9dd48dd1429d0025d926ae1f2e35bbb110bf6ee4)

BibTeX

@misc{dc495c53a48d66,
  title = {Large deviations for linear regressions — arXiv:2609.03111},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.03111},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_495c53a48d66; sha256 2b43b4e24753b1498b2f4fae9dd48dd1429d0025d926ae1f2e35bbb110bf6ee4},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.03111. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Linear regression is one of the simplest and most widely used tools to learn patterns from data: it fits a set of coefficients so that a linear combination of predictors best matches observed responses. The quality of the fit is measured by the residual sum of squares, the total squared mismatch between predictions and data, whose minimum defines the training loss. We consider Gaussian design and noise, with teacher coefficients independently drawn from a general distribution $p(\beta)$, and a general class of separable regularizers, including Ridge and Lasso. Using the zero-temperature replica method, we compute analytically the large-deviation statistics of the minimum training loss for large numbers $P$ of predictors and $N$ of observations, with $r=P/N$ fixed. The rate function we compute governs rare sample-to-sample fluctuations of the optimal loss. Extensive numerical simulations are in excellent agreement with our theory and clearly show a pronounced deviation from the Gaussian regime of typical fluctuations in the tails.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-04 in cond-mat.stat-mech).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech).
Pagina del lavoro: https://arxiv.org/abs/2609.03111 — 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 2026-10-17T02:56:38.510Z dalla pagina https://arxiv.org/catchup/cond-mat.stat-mech/2026-09-04?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).