Joint outlier detection and variable selection using discrete optimization

In regression, the quality of estimators is known to be very sensitive to the presence of spurious variables and outliers. Unfortunately, this is a frequent situation when dealing with real data. To handle outlier proneness and achieve variable selection, we propose a robust method performing the ou...

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Detalles Bibliográficos
Autores: Jammal, Mahdi, Canu, Stephane, Abdallah, Maher
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/362112
Acceso en línea:https://hdl.handle.net/2117/362112
https://dx.doi.org/10.2436/20.8080.02.109
Access Level:acceso abierto
Palabra clave:Robust optimization
statistical learning
linear regression
variable selection
outlier detection
mixed integer programming
Programació (Matemàtica)
Intel·ligència artificial
Estadística matemàtica
Classificació AMS::62 Statistics::62J Linear inference, regression
Classificació AMS::62 Statistics::62G Nonparametric inference
Classificació AMS::68 Computer science::68T Artificial intelligence
Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
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spelling Joint outlier detection and variable selection using discrete optimizationJammal, MahdiCanu, StephaneAbdallah, MaherRobust optimizationstatistical learninglinear regressionvariable selectionoutlier detectionmixed integer programmingProgramació (Matemàtica)Intel·ligència artificialEstadística matemàticaClassificació AMS::62 Statistics::62J Linear inference, regressionClassificació AMS::62 Statistics::62G Nonparametric inferenceClassificació AMS::68 Computer science::68T Artificial intelligenceClassificació AMS::90 Operations research, mathematical programming::90C Mathematical programmingÀrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàticaIn regression, the quality of estimators is known to be very sensitive to the presence of spurious variables and outliers. Unfortunately, this is a frequent situation when dealing with real data. To handle outlier proneness and achieve variable selection, we propose a robust method performing the outright rejection of discordant observations together with the selection of relevant variables. A natural way to define the corresponding optimization problem is to use the ℓ0 norm and recast it as a mixed integer optimization problem. To retrieve this global solution more efficiently, we suggest the use of additional constraints as well as a clever initialization. To this end, an efficient and scalable non-convex proximal alternate algorithm is introduced. An empirical comparison between the ℓ0 norm approach and its ℓ1 relaxation is presented as well. Results on both synthetic and real data sets provided that the mixed integer programming approach and its discrete first order warm start provide high quality solutions.Peer ReviewedInstitut d'Estadística de Catalunya20212021-06-1520222022-02-10journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/362112https://dx.doi.org/10.2436/20.8080.02.109reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3621122026-05-27T15:37:01Z
dc.title.none.fl_str_mv Joint outlier detection and variable selection using discrete optimization
title Joint outlier detection and variable selection using discrete optimization
spellingShingle Joint outlier detection and variable selection using discrete optimization
Jammal, Mahdi
Robust optimization
statistical learning
linear regression
variable selection
outlier detection
mixed integer programming
Programació (Matemàtica)
Intel·ligència artificial
Estadística matemàtica
Classificació AMS::62 Statistics::62J Linear inference, regression
Classificació AMS::62 Statistics::62G Nonparametric inference
Classificació AMS::68 Computer science::68T Artificial intelligence
Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
title_short Joint outlier detection and variable selection using discrete optimization
title_full Joint outlier detection and variable selection using discrete optimization
title_fullStr Joint outlier detection and variable selection using discrete optimization
title_full_unstemmed Joint outlier detection and variable selection using discrete optimization
title_sort Joint outlier detection and variable selection using discrete optimization
dc.creator.none.fl_str_mv Jammal, Mahdi
Canu, Stephane
Abdallah, Maher
author Jammal, Mahdi
author_facet Jammal, Mahdi
Canu, Stephane
Abdallah, Maher
author_role author
author2 Canu, Stephane
Abdallah, Maher
author2_role author
author
dc.subject.none.fl_str_mv Robust optimization
statistical learning
linear regression
variable selection
outlier detection
mixed integer programming
Programació (Matemàtica)
Intel·ligència artificial
Estadística matemàtica
Classificació AMS::62 Statistics::62J Linear inference, regression
Classificació AMS::62 Statistics::62G Nonparametric inference
Classificació AMS::68 Computer science::68T Artificial intelligence
Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
topic Robust optimization
statistical learning
linear regression
variable selection
outlier detection
mixed integer programming
Programació (Matemàtica)
Intel·ligència artificial
Estadística matemàtica
Classificació AMS::62 Statistics::62J Linear inference, regression
Classificació AMS::62 Statistics::62G Nonparametric inference
Classificació AMS::68 Computer science::68T Artificial intelligence
Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
description In regression, the quality of estimators is known to be very sensitive to the presence of spurious variables and outliers. Unfortunately, this is a frequent situation when dealing with real data. To handle outlier proneness and achieve variable selection, we propose a robust method performing the outright rejection of discordant observations together with the selection of relevant variables. A natural way to define the corresponding optimization problem is to use the ℓ0 norm and recast it as a mixed integer optimization problem. To retrieve this global solution more efficiently, we suggest the use of additional constraints as well as a clever initialization. To this end, an efficient and scalable non-convex proximal alternate algorithm is introduced. An empirical comparison between the ℓ0 norm approach and its ℓ1 relaxation is presented as well. Results on both synthetic and real data sets provided that the mixed integer programming approach and its discrete first order warm start provide high quality solutions.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-06-15
2022
2022-02-10
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/362112
https://dx.doi.org/10.2436/20.8080.02.109
url https://hdl.handle.net/2117/362112
https://dx.doi.org/10.2436/20.8080.02.109
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Institut d'Estadística de Catalunya
publisher.none.fl_str_mv Institut d'Estadística de Catalunya
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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