{"id":"https://openalex.org/W3094857757","doi":"https://doi.org/10.1137/19m1290000","title":"Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization","display_name":"Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3094857757","doi":"https://doi.org/10.1137/19m1290000","mag":"3094857757","pmid":"https://pubmed.ncbi.nlm.nih.gov/34305368"},"language":"en","primary_location":{"id":"doi:10.1137/19m1290000","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1290000","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1137/19m1290000","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100416078","display_name":"Yuxin Chen","orcid":"https://orcid.org/0000-0001-9256-5815"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuxin Chen","raw_affiliation_strings":["Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053809095","display_name":"Yuejie Chi","orcid":"https://orcid.org/0000-0002-6766-5459"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuejie Chi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA"],"raw_orcid":"https://orcid.org/0000-0002-6766-5459","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100664286","display_name":"Jianqing Fan","orcid":"https://orcid.org/0000-0003-3250-7677"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianqing Fan","raw_affiliation_strings":["Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074490643","display_name":"Cong Ma","orcid":"https://orcid.org/0000-0003-2532-0038"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cong Ma","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA"],"raw_orcid":"https://orcid.org/0000-0003-2532-0038","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100634106","display_name":"Yuling Yan","orcid":"https://orcid.org/0000-0002-5747-8182"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuling Yan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.1945,"has_fulltext":false,"cited_by_count":98,"citation_normalized_percentile":{"value":0.99315206,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"30","issue":"4","first_page":"3098","last_page":"3121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":1.0,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9833999872207642,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/matrix-completion","display_name":"Matrix completion","score":0.7151740789413452},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6543241739273071},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5795663595199585},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5719898343086243},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5261544585227966},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.515682578086853},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.5116884708404541},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.49746444821357727},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4758962392807007},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4422782063484192},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.42508959770202637},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3415992259979248},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20181307196617126},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11384570598602295},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10328933596611023},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09685233235359192}],"concepts":[{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.7151740789413452},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6543241739273071},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5795663595199585},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5719898343086243},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5261544585227966},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.515682578086853},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.5116884708404541},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.49746444821357727},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4758962392807007},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4422782063484192},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.42508959770202637},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3415992259979248},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20181307196617126},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11384570598602295},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10328933596611023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09685233235359192},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1290000","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1290000","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmid:34305368","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34305368","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM journal on optimization : a publication of the Society for Industrial and Applied Mathematics","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:8300474","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8300474","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM J Optim","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1137/19m1290000","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1290000","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1469985387","display_name":null,"funder_award_id":"N00014-19-1-2404","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G1783365290","display_name":null,"funder_award_id":"ECCS-1818571","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G248161301","display_name":null,"funder_award_id":"IIS-1900140","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2545185725","display_name":null,"funder_award_id":"DMS-1712591","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2590387755","display_name":null,"funder_award_id":"CCF-1806154","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3467583470","display_name":null,"funder_award_id":"N00014-19-1-2120","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4061742820","display_name":null,"funder_award_id":"FA9550-19-1-0030","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5945795592","display_name":null,"funder_award_id":"CCF-1907661","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5958774353","display_name":null,"funder_award_id":"R01 GM072611","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"},{"id":"https://openalex.org/G691697401","display_name":null,"funder_award_id":"R01-GM072611-12","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G7286131166","display_name":null,"funder_award_id":"DMS-1662139","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G854152385","display_name":null,"funder_award_id":"N00014-18-1-2142","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8597684915","display_name":null,"funder_award_id":"W911NF-18-1-0303","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309292","display_name":"Princeton University","ror":"https://ror.org/00hx57361"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":109,"referenced_works":["https://openalex.org/W138552861","https://openalex.org/W1492459858","https://openalex.org/W1532323952","https://openalex.org/W1545868355","https://openalex.org/W1573301526","https://openalex.org/W1878263927","https://openalex.org/W1916337001","https://openalex.org/W1976618413","https://openalex.org/W1997840761","https://openalex.org/W2000157792","https://openalex.org/W2002605354","https://openalex.org/W2003753589","https://openalex.org/W2006145698","https://openalex.org/W2011359124","https://openalex.org/W2031906930","https://openalex.org/W2040373108","https://openalex.org/W2044666483","https://openalex.org/W2047071281","https://openalex.org/W2049371785","https://openalex.org/W2058078260","https://openalex.org/W2059283452","https://openalex.org/W2060204507","https://openalex.org/W2064771273","https://openalex.org/W2077430220","https://openalex.org/W2084745075","https://openalex.org/W2095534914","https://openalex.org/W2100556411","https://openalex.org/W2103972604","https://openalex.org/W2106005123","https://openalex.org/W2111297856","https://openalex.org/W2112659545","https://openalex.org/W2116680824","https://openalex.org/W2118550318","https://openalex.org/W2120872934","https://openalex.org/W2134332047","https://openalex.org/W2138835141","https://openalex.org/W2140867429","https://openalex.org/W2142949395","https://openalex.org/W2143075842","https://openalex.org/W2143133882","https://openalex.org/W2143703915","https://openalex.org/W2144730813","https://openalex.org/W2145962650","https://openalex.org/W2146130798","https://openalex.org/W2157400927","https://openalex.org/W2158121106","https://openalex.org/W2161374719","https://openalex.org/W2166163936","https://openalex.org/W2171046470","https://openalex.org/W2189224591","https://openalex.org/W2268674159","https://openalex.org/W2339666411","https://openalex.org/W2396019715","https://openalex.org/W2426334170","https://openalex.org/W2542482481","https://openalex.org/W2566608758","https://openalex.org/W2581138301","https://openalex.org/W2598300585","https://openalex.org/W2608011286","https://openalex.org/W2611328865","https://openalex.org/W2616032753","https://openalex.org/W2739848020","https://openalex.org/W2740586183","https://openalex.org/W2768927505","https://openalex.org/W2783859821","https://openalex.org/W2785436244","https://openalex.org/W2790687101","https://openalex.org/W2810541051","https://openalex.org/W2918965983","https://openalex.org/W2950161005","https://openalex.org/W2950383522","https://openalex.org/W2953226854","https://openalex.org/W2962694024","https://openalex.org/W2962699303","https://openalex.org/W2962769133","https://openalex.org/W2962818938","https://openalex.org/W2963099043","https://openalex.org/W2963426032","https://openalex.org/W2963669167","https://openalex.org/W2963829083","https://openalex.org/W2963840025","https://openalex.org/W2963972677","https://openalex.org/W2964014592","https://openalex.org/W2965497096","https://openalex.org/W2969215180","https://openalex.org/W2982569731","https://openalex.org/W3005119431","https://openalex.org/W3043617248","https://openalex.org/W3098322757","https://openalex.org/W3098807808","https://openalex.org/W3099447760","https://openalex.org/W3099973750","https://openalex.org/W3100522009","https://openalex.org/W3101877337","https://openalex.org/W3102206315","https://openalex.org/W3102810310","https://openalex.org/W3104447032","https://openalex.org/W3104501706","https://openalex.org/W3104624268","https://openalex.org/W3104684837","https://openalex.org/W3105489725","https://openalex.org/W3106271742","https://openalex.org/W3121936541","https://openalex.org/W3123272904","https://openalex.org/W3125671026","https://openalex.org/W3128401515","https://openalex.org/W3138835833","https://openalex.org/W4230371388","https://openalex.org/W4244393449"],"related_works":["https://openalex.org/W2964006653","https://openalex.org/W2788826952","https://openalex.org/W2084983808","https://openalex.org/W1991825408","https://openalex.org/W3144354057","https://openalex.org/W4318564253","https://openalex.org/W4302315572","https://openalex.org/W1969698720","https://openalex.org/W1507830821","https://openalex.org/W2963965423"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"noisy":[3,10,62],"low-rank":[4,15],"matrix":[5,24,95],"completion:":[6],"given":[7],"partial":[8],"and":[9,26,88,122],"entries":[11],"of":[12,30,52,66,79,92,115,132,136,169,179,192],"a":[13,99,129,149],"large":[14],"matrix,":[16],"the":[17,22,31,49,61,76,86,89,93,104,116,119,123,145,170,180,188,193],"goal":[18],"is":[19,39,55,138,155],"to":[20,35,186,196],"estimate":[21],"underlying":[23],"faithfully":[25],"efficiently.":[27],"Arguably":[28],"one":[29],"most":[32],"popular":[33],"paradigms":[34],"tackle":[36],"this":[37,53,137],"problem":[38],"convex":[40,80,105,142,181,198],"relaxation,":[41],"which":[42],"achieves":[43,108],"remarkable":[44],"efficacy":[45,78],"in":[46,60,113],"practice.":[47],"However,":[48],"theoretical":[50],"support":[51],"approach":[54,107,195],"still":[56],"far":[57],"from":[58],"optimal":[59],"setting,":[63],"falling":[64],"short":[65],"explaining":[67],"its":[68,197],"empirical":[69],"success.":[70],"We":[71],"make":[72],"progress":[73],"towards":[74],"demystifying":[75],"practical":[77],"relaxation":[81,143],"vis-\u00e0-vis":[82],"random":[83],"noise.":[84,159],"When":[85],"rank":[87],"condition":[90],"number":[91],"unknown":[94],"are":[96],"bounded":[97],"by":[98,140],"constant,":[100],"we":[101,162],"demonstrate":[102],"that":[103,154,164],"programming":[106],"near-optimal":[109],"estimation":[110],"errors":[111],"-":[112,127],"terms":[114],"Euclidean":[117],"loss,":[118,121],"entrywise":[120],"spectral":[124],"norm":[125],"loss":[126],"for":[128],"wide":[130],"range":[131],"noise":[133],"levels.":[134],"All":[135],"enabled":[139],"bridging":[141],"with":[144],"nonconvex":[146,171,194],"Burer-Monteiro":[147],"approach,":[148],"seemingly":[150],"distinct":[151],"algorithmic":[152],"paradigm":[153],"provably":[156],"robust":[157],"against":[158],"More":[160],"specifically,":[161],"show":[163],"an":[165,175],"approximate":[166],"critical":[167],"point":[168],"formulation":[172],"serves":[173],"as":[174],"extremely":[176],"tight":[177],"approximation":[178],"solution,":[182],"thus":[183],"allowing":[184],"us":[185],"transfer":[187],"desired":[189],"statistical":[190],"guarantees":[191],"counterpart.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":26},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":6}],"updated_date":"2026-07-25T15:57:00.446498","created_date":"2025-10-10T00:00:00"}
