{"id":"https://openalex.org/W2743758565","doi":"https://doi.org/10.1109/tsp.2018.2824289","title":"Nonconvex Sparse Logistic Regression With Weakly Convex Regularization","display_name":"Nonconvex Sparse Logistic Regression With Weakly Convex Regularization","publication_year":2018,"publication_date":"2018-04-06","ids":{"openalex":"https://openalex.org/W2743758565","doi":"https://doi.org/10.1109/tsp.2018.2824289","mag":"2743758565"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2018.2824289","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2018.2824289","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1708.02059","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003439795","display_name":"Xinyue Shen","orcid":"https://orcid.org/0000-0001-7760-0897"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinyue Shen","raw_affiliation_strings":["Beijing National Research Center for Information Science and Technology (BNRist) and the Department of Electronic Engineering, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-7760-0897","affiliations":[{"raw_affiliation_string":"Beijing National Research Center for Information Science and Technology (BNRist) and the Department of Electronic Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100621681","display_name":"Yuantao Gu","orcid":"https://orcid.org/0000-0002-8427-1021"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuantao Gu","raw_affiliation_strings":["Beijing National Research Center for Information Science and Technology (BNRist) and the Department of Electronic Engineering, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-8427-1021","affiliations":[{"raw_affiliation_string":"Beijing National Research Center for Information Science and Technology (BNRist) and the Department of Electronic Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":5.2042,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.96596573,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"66","issue":"12","first_page":"3199","last_page":"3211"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.996399998664856,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9642000198364258,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/logistic-regression","display_name":"Logistic regression","score":0.6311475038528442},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5454741716384888},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5433995127677917},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.533146321773529},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.41154706478118896},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4093600809574127},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3870193362236023},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37711024284362793},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36585330963134766},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.35550346970558167},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3517480492591858}],"concepts":[{"id":"https://openalex.org/C151956035","wikidata":"https://www.wikidata.org/wiki/Q1132755","display_name":"Logistic regression","level":2,"score":0.6311475038528442},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5454741716384888},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5433995127677917},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.533146321773529},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.41154706478118896},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4093600809574127},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3870193362236023},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37711024284362793},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36585330963134766},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.35550346970558167},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3517480492591858},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2018.2824289","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2018.2824289","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1708.02059","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1708.02059","pdf_url":"https://arxiv.org/pdf/1708.02059","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1708.02059","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1708.02059","pdf_url":"https://arxiv.org/pdf/1708.02059","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3756907572","display_name":null,"funder_award_id":"2016YFE0201900","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4609625212","display_name":null,"funder_award_id":"61531166005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7659680391","display_name":null,"funder_award_id":"2017YFC0403600","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G7777656554","display_name":"\u56fe\u4e0a\u4fe1\u53f7\u7684\u5e7f\u4e49\u91c7\u6837\u7406\u8bba\u4e0e\u91cd\u5efa\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61571263","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}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W625557853","https://openalex.org/W1480376833","https://openalex.org/W1485433433","https://openalex.org/W1885275569","https://openalex.org/W1887132526","https://openalex.org/W1965125844","https://openalex.org/W1973520297","https://openalex.org/W1990494141","https://openalex.org/W2004544971","https://openalex.org/W2023047877","https://openalex.org/W2027197817","https://openalex.org/W2030161963","https://openalex.org/W2044297353","https://openalex.org/W2058247645","https://openalex.org/W2060430274","https://openalex.org/W2074577749","https://openalex.org/W2087684630","https://openalex.org/W2100556411","https://openalex.org/W2102984754","https://openalex.org/W2133263603","https://openalex.org/W2135046866","https://openalex.org/W2137911812","https://openalex.org/W2138145347","https://openalex.org/W2140156116","https://openalex.org/W2140721493","https://openalex.org/W2142506503","https://openalex.org/W2144073719","https://openalex.org/W2145473366","https://openalex.org/W2151499551","https://openalex.org/W2152734820","https://openalex.org/W2163761533","https://openalex.org/W2166183437","https://openalex.org/W2181470043","https://openalex.org/W2184634347","https://openalex.org/W2271221198","https://openalex.org/W2273716988","https://openalex.org/W2289145899","https://openalex.org/W2296616510","https://openalex.org/W2374886620","https://openalex.org/W2376779736","https://openalex.org/W2614442052","https://openalex.org/W2616127482","https://openalex.org/W2936995161","https://openalex.org/W2949979136","https://openalex.org/W2963248893","https://openalex.org/W2964322027","https://openalex.org/W3001495003","https://openalex.org/W3098306969","https://openalex.org/W3120740533","https://openalex.org/W4250955649","https://openalex.org/W4252328106","https://openalex.org/W4297825594","https://openalex.org/W6619863188","https://openalex.org/W6639167513","https://openalex.org/W6643732177","https://openalex.org/W6657248855","https://openalex.org/W6680344438","https://openalex.org/W6680599301","https://openalex.org/W6684111346","https://openalex.org/W6686240244","https://openalex.org/W6686534882","https://openalex.org/W6696307484","https://openalex.org/W6696497002","https://openalex.org/W6709225609","https://openalex.org/W6738096397","https://openalex.org/W6761030284","https://openalex.org/W6959508083"],"related_works":["https://openalex.org/W2129863591","https://openalex.org/W1596769710","https://openalex.org/W2923497059","https://openalex.org/W2978363435","https://openalex.org/W4394896199","https://openalex.org/W3217448422","https://openalex.org/W2351279712","https://openalex.org/W1548888553","https://openalex.org/W2908249560","https://openalex.org/W3153752017"],"abstract_inverted_index":{"In":[0],"this":[1,152],"paper,":[2],"we":[3,67],"propose":[4],"to":[5,45,100,122],"fit":[6],"a":[7,13,28,59,91,123,129,134,141,160,166],"sparse":[8,106],"logistic":[9,107,138],"regression":[10],"model":[11],"by":[12,176],"weakly":[14,29,62,104,125],"convex":[15,30,63,105,126],"regularized":[16],"nonconvex":[17],"optimization":[18],"problem.":[19],"The":[20,146],"idea":[21],"is":[22,43,98,113,120,149,163,171],"based":[23,93],"on":[24,94,136],"the":[25,36,50,69,72,82,85,89,102,117,137],"finding":[26],"that":[27],"function":[31],"as":[32,154],"an":[33,155],"approximation":[34],"of":[35,61,71,84],"\u2113":[37,53],"<sub":[38,54],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[39,55],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</sub>":[40],"pseudo":[41],"norm":[42],"able":[44],"better":[46],"induce":[47],"sparsity":[48,64],"than":[49],"commonly":[51],"used":[52,99,164],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[56],"norm.":[57],"For":[58],"class":[60],"inducing":[65],"functions,":[66],"prove":[68],"nonconvexity":[70],"corresponding":[73],"problem":[74],"and":[75,81,109,128,133,159,180],"study":[76],"its":[77,110],"local":[78,130,142],"optimality":[79,131],"conditions":[80],"choice":[83],"regularization":[86],"parameter.":[87],"Despite":[88],"nonconvexity,":[90],"method":[92,148],"proximal":[95],"gradient":[96],"descent":[97],"solve":[101],"general":[103,118],"regression,":[108],"convergence":[111,167],"behavior":[112],"studied":[114],"theoretically.":[115],"Then,":[116],"framework":[119],"applied":[121],"specific":[124],"function,":[127],"condition":[132],"bound":[135],"loss":[139],"at":[140],"optimum":[143],"are":[144],"provided.":[145],"solution":[147],"instantiated":[150],"in":[151,173],"case":[153],"iterative":[156],"firm-shrinkage":[157],"algorithm,":[158],"Nesterov":[161],"acceleration":[162],"with":[165],"guarantee.":[168],"Its":[169],"effectiveness":[170],"demonstrated":[172],"numerical":[174],"experiments":[175],"both":[177],"randomly":[178],"generated":[179],"real":[181],"datasets.":[182]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
