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Regularized least squares — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Regularized_least_squares
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T17:20:06.859Z
SHA-256 of the archived text: e96e382807f0a17d59485c361df4934a1f11cade99be71acd80b256425b8fdbb
Stable URL of this page: https://metraipolis.com/documento/dc_98ce030a19fb

How to cite

Regularized least squares — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Regularized_least_squares (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_98ce030a19fb (Metraipolis archive dc_98ce030a19fb, sha256 e96e382807f0a17d59485c361df4934a1f11cade99be71acd80b256425b8fdbb)

BibTeX

@misc{dc98ce030a19fb,
  title = {Regularized least squares — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Regularized_least_squares},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_98ce030a19fb; sha256 e96e382807f0a17d59485c361df4934a1f11cade99be71acd80b256425b8fdbb},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Regularized_least_squares. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Regularized least squares (RLS) is a family of methods for solving the least-squares problem while using regularization to further constrain the resulting solution. RLS is used for two main reasons. The first comes up when the number of variables in the linear system exceeds the number of observations. In such settings, the ordinary least-squares problem is ill-posed and is therefore impossible to fit because the associated optimization problem has infinitely many solutions. RLS allows the introduction of further constraints that uniquely determine the solution. The second reason for using RLS arises when the learned model suffers from poor generalization. RLS can be used in such cases to improve the generalizability of the model by constraining it at training time. This constraint can either force the solution to be "sparse" in some way or to reflect other prior knowledge about the problem such as information about correlations between features. A Bayesian understanding of this can be reached by showing that RLS methods are often equivalent to priors on the solution to the least-squares problem.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Linear algebra»).
Fonte: Wikipedia in inglese, voce «Regularized least squares» — https://en.wikipedia.org/wiki/Regularized_least_squares
Wikidata Q25304486 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q25304486
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Regularized_least_squares?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1375973784, consultata il 2026-10-07T16:51:20.525Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 01f74ada4023a9eb97a77d5f868d6cb82423c0da7991e104107106c28ac122a3