{"id":"https://openalex.org/W2138218159","doi":"https://doi.org/10.1080/10556780802102586","title":"Classification model selection via bilevel programming","display_name":"Classification model selection via bilevel programming","publication_year":2008,"publication_date":"2008-07-12","ids":{"openalex":"https://openalex.org/W2138218159","doi":"https://doi.org/10.1080/10556780802102586","mag":"2138218159"},"language":"en","primary_location":{"id":"doi:10.1080/10556780802102586","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780802102586","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049799303","display_name":"Gautam Kunapuli","orcid":"https://orcid.org/0000-0002-9297-2071"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"G. Kunapuli","raw_affiliation_strings":["Department of Mathematical Sciences , Rensselaer Polytechnic Institute , Troy, NY, USA","Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Rensselaer Polytechnic Institute , Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048876983","display_name":"Kristin P. Bennett","orcid":"https://orcid.org/0000-0002-8782-105X"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K.P. Bennett","raw_affiliation_strings":["Department of Mathematical Sciences , Rensselaer Polytechnic Institute , Troy, NY, USA","Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Rensselaer Polytechnic Institute , Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003645187","display_name":"Jing Hu","orcid":"https://orcid.org/0000-0001-5567-6911"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jing Hu","raw_affiliation_strings":["Department of Mathematical Sciences , Rensselaer Polytechnic Institute , Troy, NY, USA","Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Rensselaer Polytechnic Institute , Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002789695","display_name":"Jong\u2010Shi Pang","orcid":"https://orcid.org/0000-0002-2224-6787"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jong-Shi Pang","raw_affiliation_strings":["Department of Industrial and Enterprise Systems Engineering , University of Illinois at Urbana-Champaign , Urbana, IL, USA","Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Enterprise Systems Engineering , University of Illinois at Urbana-Champaign , Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5049799303"],"corresponding_institution_ids":["https://openalex.org/I165799507"],"apc_list":null,"apc_paid":null,"fwci":5.8962,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.95944697,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"23","issue":"4","first_page":"475","last_page":"489"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9656000137329102,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9203000068664551,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.7854831218719482},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.6877381205558777},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6454697847366333},{"id":"https://openalex.org/keywords/model-selection","display_name":"Model selection","score":0.43190521001815796},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.42734748125076294},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1883203685283661},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.06177741289138794}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.7854831218719482},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.6877381205558777},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6454697847366333},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.43190521001815796},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42734748125076294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1883203685283661},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.06177741289138794}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556780802102586","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780802102586","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309013","display_name":"North Dakota State University","ror":"https://ror.org/05h1bnb22"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W217831350","https://openalex.org/W1510073064","https://openalex.org/W1543439990","https://openalex.org/W1588628884","https://openalex.org/W1966095601","https://openalex.org/W1976886395","https://openalex.org/W1985195207","https://openalex.org/W1990381576","https://openalex.org/W1997138910","https://openalex.org/W2017337590","https://openalex.org/W2034039293","https://openalex.org/W2035720976","https://openalex.org/W2037678919","https://openalex.org/W2042838878","https://openalex.org/W2048799772","https://openalex.org/W2055586095","https://openalex.org/W2074352998","https://openalex.org/W2082988498","https://openalex.org/W2087472326","https://openalex.org/W2115729631","https://openalex.org/W2119638507","https://openalex.org/W2119821739","https://openalex.org/W2122825543","https://openalex.org/W2128255043","https://openalex.org/W2130698119","https://openalex.org/W2133958955","https://openalex.org/W2135046866","https://openalex.org/W2143426320","https://openalex.org/W2155640943","https://openalex.org/W2156909104","https://openalex.org/W2158001550","https://openalex.org/W2166758048","https://openalex.org/W2171126500","https://openalex.org/W2254218369","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4237041411","https://openalex.org/W1588628884","https://openalex.org/W1994745260","https://openalex.org/W2012267561","https://openalex.org/W2382404424","https://openalex.org/W4300511218","https://openalex.org/W3018909868","https://openalex.org/W3040509871","https://openalex.org/W4381571012"],"abstract_inverted_index":{"Support":[0],"vector":[1],"machines":[2],"and":[3],"related":[4],"classification":[5,34,73],"models":[6,143],"require":[7],"the":[8,22,28,32,37,52,56,63,72,84,92,96,102,140,150],"solution":[9],"of":[10,31,36,59,98,142,152],"convex":[11],"optimization":[12,41,123],"problems":[13],"that":[14,71],"have":[15],"one":[16],"or":[17,80],"more":[18,129],"regularization":[19],"hyper-parameters.":[20,86,146],"Typically,":[21],"hyper-parameters":[23],"are":[24,78],"selected":[25,85],"to":[26,67,110],"minimize":[27],"cross-validated":[29],"estimates":[30],"out-of-sample":[33],"error":[35],"model.":[38],"This":[39,125],"cross-validation":[40,64],"problem":[42,107],"can":[43],"be":[44],"formulated":[45],"as":[46],"a":[47,111],"bilevel":[48,93,106],"program":[49,94,113],"in":[50,91,95,101,138,158],"which":[51,118],"outer-level":[53],"objective":[54],"minimizes":[55],"average":[57],"number":[58],"misclassified":[60],"points":[61],"across":[62],"folds,":[65],"subject":[66],"inner-level":[68],"constraints":[69,100],"such":[70],"functions":[74],"for":[75,83,155],"each":[76],"fold":[77],"(exactly":[79],"nearly)":[81],"optimal":[82],"Feature":[87],"selection":[88,157],"is":[89,108,119,127],"included":[90],"form":[97],"bound":[99],"weights.":[103],"The":[104],"resulting":[105],"converted":[109],"mathematical":[112],"with":[114,144],"linear":[115],"equilibrium":[116],"constraints,":[117],"solved":[120],"using":[121],"state-of-the-art":[122],"methods.":[124],"approach":[126,154],"significantly":[128],"versatile":[130],"than":[131],"commonly":[132],"used":[133],"grid":[134],"search":[135],"procedures,":[136],"enabling,":[137],"particular,":[139],"use":[141],"many":[145],"Numerical":[147],"results":[148],"demonstrate":[149],"practicality":[151],"this":[153],"model":[156],"machine":[159],"learning.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":10},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}
