{"id":"https://openalex.org/W3120924119","doi":"https://doi.org/10.1109/cdc42340.2020.9303777","title":"On the Influence of Ill-conditioned Regression Matrix on Hyper-parameter Estimators for Kernel-based Regularization Methods","display_name":"On the Influence of Ill-conditioned Regression Matrix on Hyper-parameter Estimators for Kernel-based Regularization Methods","publication_year":2020,"publication_date":"2020-12-14","ids":{"openalex":"https://openalex.org/W3120924119","doi":"https://doi.org/10.1109/cdc42340.2020.9303777","mag":"3120924119"},"language":"en","primary_location":{"id":"doi:10.1109/cdc42340.2020.9303777","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc42340.2020.9303777","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 59th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5075622665","display_name":"Yue Ju","orcid":"https://orcid.org/0009-0006-4437-1833"},"institutions":[{"id":"https://openalex.org/I4210099586","display_name":"Shenzhen Research Institute of Big Data","ror":"https://ror.org/00z1gwf89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099586"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Ju","raw_affiliation_strings":["School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I4210099586","https://openalex.org/I4210116924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102935603","display_name":"Tianshi Chen","orcid":"https://orcid.org/0000-0001-8655-2655"},"institutions":[{"id":"https://openalex.org/I4210099586","display_name":"Shenzhen Research Institute of Big Data","ror":"https://ror.org/00z1gwf89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099586"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianshi Chen","raw_affiliation_strings":["School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I4210099586","https://openalex.org/I4210116924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016633088","display_name":"Biqiang Mu","orcid":"https://orcid.org/0000-0003-1340-7830"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Biqiang Mu","raw_affiliation_strings":["Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078405221","display_name":"Lennart Ljung","orcid":"https://orcid.org/0000-0003-4881-8955"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Lennart Ljung","raw_affiliation_strings":["Division of Automatic Control, Linkoping University, Linkoping, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Automatic Control, Linkoping University, Linkoping, Sweden","institution_ids":["https://openalex.org/I102134673"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0344,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.91017964,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"300","last_page":"305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9991999864578247,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5950925350189209},{"id":"https://openalex.org/keywords/hyperparameter","display_name":"Hyperparameter","score":0.5774655938148499},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5546167492866516},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5533181428909302},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4645163118839264},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44540515542030334},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4359718859195709},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4354630708694458},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3769489526748657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2682008743286133},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26492202281951904},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22811821103096008}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5950925350189209},{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.5774655938148499},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5546167492866516},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5533181428909302},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4645163118839264},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44540515542030334},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4359718859195709},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4354630708694458},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3769489526748657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2682008743286133},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26492202281951904},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22811821103096008},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc42340.2020.9303777","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc42340.2020.9303777","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 59th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W178056938","https://openalex.org/W1862263964","https://openalex.org/W1965324089","https://openalex.org/W1990381576","https://openalex.org/W2021065610","https://openalex.org/W2092766760","https://openalex.org/W2161083632","https://openalex.org/W2163204284","https://openalex.org/W2963774371","https://openalex.org/W3023876375","https://openalex.org/W6777181708"],"related_works":["https://openalex.org/W2140186469","https://openalex.org/W4390421286","https://openalex.org/W4280563792","https://openalex.org/W4389724018","https://openalex.org/W4318719684","https://openalex.org/W3183136280","https://openalex.org/W4318559728","https://openalex.org/W2359063982","https://openalex.org/W2360658320","https://openalex.org/W3172664294"],"abstract_inverted_index":{"In":[0,169],"this":[1],"paper,":[2],"we":[3,33,47,126,140,176],"study":[4],"the":[5,17,21,26,35,39,52,57,60,65,73,90,96,114,128,132,151,156,159,164,172,179,203],"influence":[6,58,157],"of":[7,38,42,59,85,99,117,123,131,135,158,182,188,193],"ill-conditioned":[8,61,160],"regression":[9,62,91,161,174],"matrix":[10,63,92,162],"on":[11,64,163],"two":[12],"hyper-parameter":[13],"estimation":[14],"methods":[15],"for":[16,70,76,171],"kernel-based":[18],"regularization":[19],"method:":[20],"empirical":[22],"Bayes":[23],"(EB)":[24],"and":[25,44,46,93,137,139,149],"Stein's":[27],"unbiased":[28],"risk":[29],"estimator":[30],"(SURE).":[31],"First,":[32],"consider":[34,127],"convergence":[36,54,129,153],"rate":[37,55,130],"cost":[40,115],"functions":[41],"EB":[43,136,189],"SURE,":[45,138],"find":[48,141],"that":[49,84,105,122,142,178,187],"they":[50,143],"have":[51,150],"same":[53,152],"but":[56,155],"scale":[66,74,165],"factor":[67,75,81,166,192],"are":[68,144,167],"different:":[69],"upper":[71],"bounds,":[72],"SURE":[77,118,183],"contains":[78],"one":[79],"more":[80],"cond(\u03a6T\u03a6)":[82,111,196],"than":[83,121,186],"EB,":[86],"where":[87,200],"\u03a6":[88,107],"is":[89,108,112,202],"cond(\u00b7)":[94],"denotes":[95],"condition":[97],"number":[98],"a":[100,191],"matrix.":[101],"This":[102],"finding":[103],"indicates":[104],"when":[106],"ill-conditioned,":[109],"i.e.,":[110],"large,":[113],"function":[116],"converges":[119,184],"slower":[120,185],"EB.":[124],"Then":[125],"optimal":[133,180],"hyper-parameters":[134],"both":[145],"asymptotically":[146],"normally":[147],"distributed":[148],"rate,":[154],"different.":[168],"particular,":[170],"ridge":[173],"case,":[175],"show":[177],"hyperparameter":[181],"with":[190],"1/n2,":[194],"as":[195],"goes":[197],"to":[198],"\u221e,":[199],"n":[201],"FIR":[204],"model":[205],"order.":[206]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
