{"id":"https://openalex.org/W4407025683","doi":"https://doi.org/10.1109/tit.2025.3537594","title":"Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network","display_name":"Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network","publication_year":2025,"publication_date":"2025-01-31","ids":{"openalex":"https://openalex.org/W4407025683","doi":"https://doi.org/10.1109/tit.2025.3537594"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2025.3537594","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3537594","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5112906233","display_name":"Zhao Ding","orcid":null},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhao Ding","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China"],"raw_orcid":"https://orcid.org/0009-0002-5151-7264","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062728677","display_name":"Chenguang Duan","orcid":null},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenguang Duan","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China"],"raw_orcid":"https://orcid.org/0009-0009-0815-6281","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080185313","display_name":"Yuling Jiao","orcid":"https://orcid.org/0000-0003-2762-0421"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]},{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuling Jiao","raw_affiliation_strings":["School of Artificial Intelligence, the National Center for Applied Mathematics in Hubei, Hubei Key Laboratory of Computational Science, and the School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China","Hubei Key Laboratory of Computational Science, and School of Mathematics and Statistics, School of Artificial Intelligence, National Center for Applied Mathematics in Hubei, Wuhan University, Wuhan, Hubei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, the National Center for Applied Mathematics in Hubei, Hubei Key Laboratory of Computational Science, and the School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China","institution_ids":["https://openalex.org/I75900474"]},{"raw_affiliation_string":"Hubei Key Laboratory of Computational Science, and School of Mathematics and Statistics, School of Artificial Intelligence, National Center for Applied Mathematics in Hubei, Wuhan University, Wuhan, Hubei, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057896052","display_name":"Jerry Zhijian Yang","orcid":"https://orcid.org/0000-0002-0402-4056"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]},{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jerry Zhijian Yang","raw_affiliation_strings":["National Center for Applied Mathematics in Hubei, Wuhan Institute for Math &#x0026; Al, the School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, Hubei, Hubei, China","Wuhan Institute for Math &#x0026; Al, School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, National Center for Applied Mathematics in Hubei, Wuhan University, Wuhan, Hubei, China"],"raw_orcid":"https://orcid.org/0000-0002-0402-4056","affiliations":[{"raw_affiliation_string":"National Center for Applied Mathematics in Hubei, Wuhan Institute for Math &#x0026; Al, the School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, Hubei, Hubei, China","institution_ids":["https://openalex.org/I75900474"]},{"raw_affiliation_string":"Wuhan Institute for Math &#x0026; Al, School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, National Center for Applied Mathematics in Hubei, Wuhan University, Wuhan, Hubei, China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9349,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.71385837,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"71","issue":"4","first_page":"2955","last_page":"2981"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.6478000283241272,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.6478000283241272,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12169","display_name":"Non-Destructive Testing Techniques","score":0.618399977684021,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10320","display_name":"Neural Networks and Applications","score":0.6158000230789185,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.5461035370826721},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5364663600921631},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5290395617485046},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.5033997893333435},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49654608964920044},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.48178717494010925},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.46015292406082153},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4450216591358185},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4399564862251282},{"id":"https://openalex.org/keywords/feature-selection","display_name":"Feature selection","score":0.42175018787384033},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4132747948169708},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.4119046628475189},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3182825446128845},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13153600692749023}],"concepts":[{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5461035370826721},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5364663600921631},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5290395617485046},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5033997893333435},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49654608964920044},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.48178717494010925},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.46015292406082153},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4450216591358185},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4399564862251282},{"id":"https://openalex.org/C148483581","wikidata":"https://www.wikidata.org/wiki/Q446488","display_name":"Feature selection","level":2,"score":0.42175018787384033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4132747948169708},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.4119046628475189},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3182825446128845},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13153600692749023},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2025.3537594","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3537594","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1739774501","display_name":null,"funder_award_id":"No. 12371441","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G228834145","display_name":null,"funder_award_id":"U24A2002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5663184433","display_name":null,"funder_award_id":"12371441","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6284605730","display_name":null,"funder_award_id":"No. 2024YFA1014202","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G6616829470","display_name":null,"funder_award_id":"No. 12125103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7740712931","display_name":null,"funder_award_id":"No. U24A2002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8797177794","display_name":null,"funder_award_id":"12125103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":91,"referenced_works":["https://openalex.org/W1484867920","https://openalex.org/W1511694993","https://openalex.org/W1524622012","https://openalex.org/W1584847342","https://openalex.org/W1586623601","https://openalex.org/W1597926580","https://openalex.org/W1790623579","https://openalex.org/W1820125862","https://openalex.org/W1988889362","https://openalex.org/W1989412209","https://openalex.org/W1990334093","https://openalex.org/W1998560353","https://openalex.org/W2032708346","https://openalex.org/W2038845890","https://openalex.org/W2057638322","https://openalex.org/W2058262390","https://openalex.org/W2065274576","https://openalex.org/W2073040595","https://openalex.org/W2074632788","https://openalex.org/W2082319640","https://openalex.org/W2086104794","https://openalex.org/W2091406882","https://openalex.org/W2096061680","https://openalex.org/W2103038618","https://openalex.org/W2106972536","https://openalex.org/W2112594540","https://openalex.org/W2118021080","https://openalex.org/W2144366961","https://openalex.org/W2144732271","https://openalex.org/W2155393745","https://openalex.org/W2465206646","https://openalex.org/W2573774505","https://openalex.org/W2749772809","https://openalex.org/W2760972773","https://openalex.org/W2768346313","https://openalex.org/W2920824121","https://openalex.org/W2946302218","https://openalex.org/W2949883708","https://openalex.org/W2962821226","https://openalex.org/W2963146412","https://openalex.org/W2963184067","https://openalex.org/W2963341057","https://openalex.org/W2965192329","https://openalex.org/W2969750612","https://openalex.org/W2972999963","https://openalex.org/W2973682480","https://openalex.org/W2984353870","https://openalex.org/W3035281012","https://openalex.org/W3129542174","https://openalex.org/W3156262913","https://openalex.org/W3201938571","https://openalex.org/W3204236384","https://openalex.org/W3204708751","https://openalex.org/W4205354563","https://openalex.org/W4205462863","https://openalex.org/W4211030719","https://openalex.org/W4220826888","https://openalex.org/W4237171445","https://openalex.org/W4249716558","https://openalex.org/W4298876635","https://openalex.org/W4302599714","https://openalex.org/W4321513905","https://openalex.org/W4322622870","https://openalex.org/W4353046719","https://openalex.org/W4380490515","https://openalex.org/W4388446652","https://openalex.org/W6604389503","https://openalex.org/W6674794121","https://openalex.org/W6675747103","https://openalex.org/W6676377354","https://openalex.org/W6676667496","https://openalex.org/W6688386640","https://openalex.org/W6715221174","https://openalex.org/W6732517885","https://openalex.org/W6735913928","https://openalex.org/W6738369334","https://openalex.org/W6738706147","https://openalex.org/W6739448629","https://openalex.org/W6748230616","https://openalex.org/W6748651261","https://openalex.org/W6751002639","https://openalex.org/W6753969644","https://openalex.org/W6759976280","https://openalex.org/W6764621852","https://openalex.org/W6777808597","https://openalex.org/W6782866703","https://openalex.org/W6795925347","https://openalex.org/W6796131327","https://openalex.org/W6851752577","https://openalex.org/W6856729087","https://openalex.org/W6980693771"],"related_works":["https://openalex.org/W2362588090","https://openalex.org/W31220157","https://openalex.org/W2312753042","https://openalex.org/W4289356671","https://openalex.org/W2389155397","https://openalex.org/W2165884543","https://openalex.org/W3186837933","https://openalex.org/W2368989808","https://openalex.org/W1969346022","https://openalex.org/W2034959125"],"abstract_inverted_index":{"We":[0],"propose":[1],"SDORE,":[2],"a":[3,56,79],"<underline":[4,7,13],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,8,11,14,67],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">s</u>emi-supervised":[6],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d</u>eep":[9],"S<underline":[10],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">o</u>bolev":[12],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">re</u>gressor,":[15],"for":[16,82,102],"the":[17,21,36,44,47,60,73,83,90,108,111,116,127,134,143],"nonparametric":[18,154],"estimation":[19],"of":[20,46,59,63,92,110,119,129,159,167],"underlying":[22],"regression":[23,144],"function":[24,145],"and":[25,106,146],"its":[26,147],"gradient.":[27],"SDORE":[28,64,132,160],"employs":[29],"deep":[30],"ReQU":[31],"neural":[32,112,137],"networks":[33],"to":[34],"minimize":[35],"empirical":[37],"risk":[38],"with":[39,149],"gradient":[40,86],"norm":[41],"regularization,":[42],"allowing":[43],"approximation":[45],"regularization":[48,104],"term":[49],"by":[50],"unlabeled":[51,121],"data.":[52],"Our":[53],"study":[54],"includes":[55],"thorough":[57],"analysis":[58],"convergence":[61,80],"rates":[62],"in":[65,89,123],"<inline-formula":[66],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[68],"<tex-math":[69],"notation=\"LaTeX\">$L^{2}$":[70],"</tex-math></inline-formula>-norm,":[71],"achieving":[72],"minimax":[74],"optimality.":[75],"Further,":[76],"we":[77],"establish":[78],"rate":[81],"associated":[84],"plug-in":[85],"estimator,":[87],"even":[88],"presence":[91],"significant":[93],"domain":[94],"shift.":[95],"These":[96],"theoretical":[97],"findings":[98],"offer":[99],"valuable":[100],"insights":[101],"selecting":[103],"parameters":[105],"determining":[107],"size":[109],"network,":[113],"while":[114],"showcasing":[115],"provable":[117,136],"advantage":[118],"leveraging":[120],"data":[122],"semi-supervised":[124],"learning.":[125],"To":[126],"best":[128],"our":[130],"knowledge,":[131],"is":[133,161],"first":[135],"network-based":[138],"approach":[139],"that":[140],"simultaneously":[141],"estimates":[142],"gradient,":[148],"diverse":[150],"applications":[151],"such":[152],"as":[153],"variable":[155],"selection.":[156],"The":[157],"effectiveness":[158],"validated":[162],"through":[163],"an":[164],"extensive":[165],"range":[166],"numerical":[168],"simulations.":[169]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
