{"id":"https://openalex.org/W2768353504","doi":"https://doi.org/10.1109/tit.2017.2773474","title":"Convex and Nonconvex Formulations for Mixed Regression With Two Components: Minimax Optimal Rates","display_name":"Convex and Nonconvex Formulations for Mixed Regression With Two Components: Minimax Optimal Rates","publication_year":2017,"publication_date":"2017-11-14","ids":{"openalex":"https://openalex.org/W2768353504","doi":"https://doi.org/10.1109/tit.2017.2773474","mag":"2768353504"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2773474","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2773474","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/A5060774236","display_name":"Yudong Chen","orcid":"https://orcid.org/0000-0002-6416-5635"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yudong Chen","raw_affiliation_strings":["School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA"],"affiliations":[{"raw_affiliation_string":"School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102976295","display_name":"Xinyang Yi","orcid":"https://orcid.org/0000-0002-0959-4859"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xinyang Yi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053978837","display_name":"Constantine Caramanis","orcid":"https://orcid.org/0000-0001-9939-8378"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Constantine Caramanis","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060774236"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":1.9754,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.85648808,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"64","issue":"3","first_page":"1738","last_page":"1766"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.994700014591217,"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/minimax","display_name":"Minimax","score":0.8783735632896423},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5904155373573303},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.578782320022583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5446240305900574},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5030044913291931},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.46780160069465637},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.46512529253959656},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"Sample complexity","score":0.4548916518688202},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4320119023323059},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34561091661453247},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11621955037117004},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10435435175895691}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.8783735632896423},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5904155373573303},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.578782320022583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5446240305900574},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5030044913291931},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.46780160069465637},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.46512529253959656},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.4548916518688202},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4320119023323059},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34561091661453247},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11621955037117004},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10435435175895691},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2017.2773474","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2773474","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":[],"awards":[{"id":"https://openalex.org/G124291174","display_name":null,"funder_award_id":"CCF-1704828","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7280520362","display_name":null,"funder_award_id":"EECS-1056028","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8906074556","display_name":null,"funder_award_id":"CCF-1116955","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8963373266","display_name":null,"funder_award_id":"CNS-1302435","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309624","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1503100111","https://openalex.org/W1511694993","https://openalex.org/W1524622012","https://openalex.org/W1538452572","https://openalex.org/W1781773254","https://openalex.org/W1854990296","https://openalex.org/W1993962865","https://openalex.org/W2014565165","https://openalex.org/W2023770210","https://openalex.org/W2032291279","https://openalex.org/W2049633694","https://openalex.org/W2053742104","https://openalex.org/W2060195349","https://openalex.org/W2078397124","https://openalex.org/W2091369174","https://openalex.org/W2099111195","https://openalex.org/W2101522492","https://openalex.org/W2105724942","https://openalex.org/W2107411554","https://openalex.org/W2118550318","https://openalex.org/W2124428910","https://openalex.org/W2133105246","https://openalex.org/W2137945041","https://openalex.org/W2138142480","https://openalex.org/W2138967244","https://openalex.org/W2152461258","https://openalex.org/W2162451874","https://openalex.org/W2169501582","https://openalex.org/W2542482481","https://openalex.org/W2566240941","https://openalex.org/W2611328865","https://openalex.org/W2950741027","https://openalex.org/W2962686239","https://openalex.org/W2962737134","https://openalex.org/W2963443408","https://openalex.org/W2965497096","https://openalex.org/W3098045837","https://openalex.org/W3098494111","https://openalex.org/W3099880660","https://openalex.org/W3101651037","https://openalex.org/W4231920484","https://openalex.org/W6638071513","https://openalex.org/W6678489871","https://openalex.org/W6680662047","https://openalex.org/W6686540645"],"related_works":["https://openalex.org/W2397544591","https://openalex.org/W4376639527","https://openalex.org/W1991417304","https://openalex.org/W2132876566","https://openalex.org/W2990709181","https://openalex.org/W1969276875","https://openalex.org/W2788738055","https://openalex.org/W2950049300","https://openalex.org/W3153752017","https://openalex.org/W4299895404"],"abstract_inverted_index":{"We":[0,14,57],"consider":[1],"the":[2,23,46,82,101,111,120,124],"mixed":[3],"regression":[4],"problem":[5,118],"with":[6,89],"two":[7],"components,":[8],"under":[9,34],"adversarial":[10],"and":[11,38,53,95],"stochastic":[12,54],"noise.":[13],"give":[15,59],"a":[16,29,76,114],"convex":[17],"optimization":[18],"formulation":[19,31],"that":[20,32,69,110],"provably":[21],"recovers":[22],"true":[24],"solution,":[25],"as":[26,28],"well":[27],"nonconvex":[30],"works":[33],"more":[35,116],"general":[36],"settings":[37],"remains":[39],"tractable.":[40],"Upper":[41],"bounds":[42,63,91],"are":[43],"provided":[44],"on":[45,92],"recovery":[47,88,93],"errors":[48,94],"for":[49],"both":[50],"arbitrary":[51],"noise":[52,55],"models.":[56],"also":[58],"matching":[60],"minimax":[61],"lower":[62],"(up":[64],"to":[65],"log":[66],"factors),":[67],"showing":[68],"our":[70,106],"algorithm":[71,85],"is":[72],"information-theoretical":[73],"optimal":[74],"in":[75,119],"precise":[77],"sense.":[78],"Our":[79],"results":[80,108],"represent":[81],"first":[83],"tractable":[84],"guaranteeing":[86],"successful":[87],"tight":[90],"sample":[96],"complexity.":[97],"Moreover,":[98],"we":[99],"pinpoint":[100],"statistical":[102],"cost":[103],"of":[104],"mixtures:":[105],"minimax-optimal":[107],"indicate":[109],"mixture":[112],"poses":[113],"fundamentally":[115],"difficult":[117],"low-SNR":[121],"regime,":[122],"where":[123],"learning":[125],"rate":[126],"changes.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}