About: Regularized least squares

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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.

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rdfs:label	Regularized least squares (en)
rdfs:comment	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. (en)
dcterms:subject	Linear algebra Inverse problems Least squares
Wikipage page ID	48803892 (xsd:integer)
Wikipage revision ID	1123084932 (xsd:integer)
Link from a Wikipage to another Wikipage	Bayesian inference Elastic net regularization Mixture (probability) Mercer's theorem Total variation regularization Regularized least squares Ridge regression L0 norm L2 norm Convex optimization Covariance Gauss–Markov theorem Generalization error Representer theorem Symmetric Machine learning Cholesky decomposition Complete metric space Orthonormal basis Laplace distribution Lasso (statistics) Least-angle regression Least squares Log-likelihood Linear algebra Normal distribution Gaussian distribution Prior probability Quadratic programming Rank (linear algebra) Regularization (mathematics) Residual sum of squares Hilbert space Hinge loss Inverse problems Covariance matrix L1 norm Support vector machine Least squares Tikhonov regularization Positive definite Mean square error Ill-posed problem Ordinary least squares Symmetric function Kernel trick Proximal gradient method Backward elimination Forward selection Gaussian kernel Support vector regression Least angle regression Prior distribution Lasso regression Positive-definite kernel function dbr:Epsilon-insensitive_loss dbr:Spike_and_slab dbr:Split–Bregman_method
Link from a Wikipage to an external page	https://www.mit.edu/~9.520/fall15/slides/class06/class06_RLSSVM.pdf https://www.mit.edu/~9.520/spring07/Classes/rlsslides.pdf http://www.stanford.edu/~hastie/TALKS/enet_talk.pdf
sameAs	Regularized least squares Regularized least squares Regularized least squares
dbp:wikiPageUsesTemplate	dbt:Regression_bar dbt:! dbt:Anchor dbt:Further dbt:Main dbt:Reflist dbt:Summarize
has abstract	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. (en)
gold:hypernym	Family
prov:wasDerivedFrom	wikipedia-en:Regularized_least_squares?oldid=1123084932&ns=0
page length (characters) of wiki page	23384 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Regularized_least_squares
is Link from a Wikipage to another Wikipage of	Bayesian linear regression Bayesian interpretation of kernel regularization Regularized least squares Degrees of freedom (statistics) Low-rank matrix approximations Linear least squares RLS Regularization (mathematics) Weak supervision Regularized least-squares Regularized regression Penalized estimation Penalized least squares Penalized regression Least squares regularization
is Wikipage redirect of	Regularized least-squares Regularized regression

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