This HTML5 document contains 83 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
yago-reshttp://yago-knowledge.org/resource/
dbohttp://dbpedia.org/ontology/
foafhttp://xmlns.com/foaf/0.1/
n17https://global.dbpedia.org/id/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
n5https://www.mit.edu/~9.520/fall15/slides/class06/
n7http://www.stanford.edu/~hastie/TALKS/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
wikipedia-enhttp://en.wikipedia.org/wiki/
dbchttp://dbpedia.org/resource/Category:
dbphttp://dbpedia.org/property/
provhttp://www.w3.org/ns/prov#
xsdhhttp://www.w3.org/2001/XMLSchema#
n6https://www.mit.edu/~9.520/spring07/Classes/
wikidatahttp://www.wikidata.org/entity/
goldhttp://purl.org/linguistics/gold/
dbrhttp://dbpedia.org/resource/

Statements

Subject Item
dbr:Regularized_least_squares
rdfs:label
Regularized least squares
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.
dcterms:subject
dbc:Inverse_problems dbc:Least_squares dbc:Linear_algebra
dbo:wikiPageID
48803892
dbo:wikiPageRevisionID
1123084932
dbo:wikiPageWikiLink
dbr:Representer_theorem dbr:Forward_selection dbr:Epsilon-insensitive_loss dbr:Rank_(linear_algebra) dbr:Quadratic_programming dbr:Tikhonov_regularization dbr:Bayesian_inference dbc:Inverse_problems dbr:Positive-definite_kernel_function dbr:Residual_sum_of_squares dbr:Mixture_(probability) dbc:Least_squares dbr:Support_vector_machine dbr:Prior_distribution dbr:Gauss–Markov_theorem dbr:Support_vector_regression dbr:Hinge_loss dbr:Gaussian_distribution dbr:Mean_square_error dbr:Orthonormal_basis dbr:Positive_definite dbr:Convex_optimization dbr:Elastic_net_regularization dbr:Lasso_(statistics) dbr:L0_norm dbr:Proximal_gradient_method dbr:Spike_and_slab dbr:Covariance_matrix dbr:Split–Bregman_method dbr:Normal_distribution dbr:Hilbert_space dbr:Lasso_regression dbr:Log-likelihood dbr:Complete_metric_space dbr:Backward_elimination dbr:L1_norm dbr:Cholesky_decomposition dbr:Covariance dbr:Ridge_regression dbr:Generalization_error dbr:Prior_probability dbr:Regularized_least_squares dbr:L2_norm dbr:Gaussian_kernel dbr:Mercer's_theorem dbr:Least_squares dbr:Laplace_distribution dbr:Machine_learning dbr:Kernel_trick dbr:Symmetric dbr:Total_variation_regularization dbr:Symmetric_function dbr:Regularization_(mathematics) dbc:Linear_algebra dbr:Least_angle_regression dbr:Ordinary_least_squares dbr:Ill-posed_problem dbr:Least-angle_regression
dbo:wikiPageExternalLink
n5:class06_RLSSVM.pdf n6:rlsslides.pdf n7:enet_talk.pdf
owl:sameAs
wikidata:Q25304486 n17:2Npkv yago-res:Regularized_least_squares
dbp:wikiPageUsesTemplate
dbt:! dbt:Anchor dbt:Further dbt:Summarize dbt:Main dbt:Regression_bar dbt:Reflist
dbo: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.
gold:hypernym
dbr:Family
prov:wasDerivedFrom
wikipedia-en:Regularized_least_squares?oldid=1123084932&ns=0
dbo:wikiPageLength
23384
foaf:isPrimaryTopicOf
wikipedia-en:Regularized_least_squares