{"id":"https://openalex.org/W2788506892","doi":"https://doi.org/10.1109/tit.2021.3050427","title":"Nonconvex Matrix Factorization From Rank-One Measurements","display_name":"Nonconvex Matrix Factorization From Rank-One Measurements","publication_year":2021,"publication_date":"2021-01-10","ids":{"openalex":"https://openalex.org/W2788506892","doi":"https://doi.org/10.1109/tit.2021.3050427","mag":"2788506892"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3050427","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3050427","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1802.06286","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011866457","display_name":"Yuan\u2010Xin Li","orcid":"https://orcid.org/0000-0003-4136-0961"},"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":"Yuanxin Li","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","[Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"[Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA]","institution_ids":["https://openalex.org/I74973139"]}]},{"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/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cong Ma","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of California at Berkeley, Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of California at Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","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, USA","Department of Electrical Engineering Princeton University Princeton NJ USA"],"raw_orcid":"https://orcid.org/0000-0001-9256-5815","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Department of Electrical Engineering Princeton University Princeton NJ USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","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, USA","[Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 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, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"[Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA]","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.76,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.61016228,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"67","issue":"3","first_page":"1928","last_page":"1950"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9940000176429749,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.8048540353775024},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5728532075881958},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5360318422317505},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5141608715057373},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5075670480728149},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4562850892543793},{"id":"https://openalex.org/keywords/quantum-tomography","display_name":"Quantum tomography","score":0.4552740454673767},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45428159832954407},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.45301133394241333},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4501972198486328},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4469428062438965},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4345327615737915},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.41112220287323},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.29838797450065613},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2282678782939911},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.20165425539016724},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.1153954267501831},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.090920090675354}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.8048540353775024},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5728532075881958},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5360318422317505},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5141608715057373},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5075670480728149},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4562850892543793},{"id":"https://openalex.org/C166834278","wikidata":"https://www.wikidata.org/wiki/Q4218494","display_name":"Quantum tomography","level":4,"score":0.4552740454673767},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45428159832954407},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.45301133394241333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4501972198486328},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4469428062438965},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4345327615737915},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.41112220287323},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29838797450065613},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2282678782939911},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.20165425539016724},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.1153954267501831},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.090920090675354},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2021.3050427","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3050427","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"},{"id":"pmh:oai:arXiv.org:1802.06286","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.06286","pdf_url":"https://arxiv.org/pdf/1802.06286","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":"","raw_type":"text"},{"id":"mag:2788506892","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1802.06286","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1802.06286","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1802.06286","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1802.06286","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.06286","pdf_url":"https://arxiv.org/pdf/1802.06286","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":"","raw_type":"text"},"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/G1580069250","display_name":null,"funder_award_id":"CCF-1901199","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/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/G2767619165","display_name":null,"funder_award_id":"FA9550-15-1-0205","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"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/G3901903351","display_name":null,"funder_award_id":"DMS-2014279","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4232129389","display_name":null,"funder_award_id":"CAREER ECCS-1818571","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"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/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/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W148829298","https://openalex.org/W1560153690","https://openalex.org/W1970377488","https://openalex.org/W2078397124","https://openalex.org/W2088911135","https://openalex.org/W2091369174","https://openalex.org/W2091775960","https://openalex.org/W2116680824","https://openalex.org/W2133105246","https://openalex.org/W2142949395","https://openalex.org/W2145080587","https://openalex.org/W2150657707","https://openalex.org/W2152565782","https://openalex.org/W2155434899","https://openalex.org/W2162451874","https://openalex.org/W2169501582","https://openalex.org/W2286769582","https://openalex.org/W2462226338","https://openalex.org/W2511406830","https://openalex.org/W2514817908","https://openalex.org/W2542482481","https://openalex.org/W2581138301","https://openalex.org/W2593299318","https://openalex.org/W2598300585","https://openalex.org/W2625063094","https://openalex.org/W2725016515","https://openalex.org/W2739848020","https://openalex.org/W2742156137","https://openalex.org/W2768927505","https://openalex.org/W2782005967","https://openalex.org/W2783859821","https://openalex.org/W2790687101","https://openalex.org/W2798291370","https://openalex.org/W2887509927","https://openalex.org/W2918965983","https://openalex.org/W2952469246","https://openalex.org/W2962761770","https://openalex.org/W2962999772","https://openalex.org/W2963077884","https://openalex.org/W2963417959","https://openalex.org/W2963519307","https://openalex.org/W2963583445","https://openalex.org/W2963731874","https://openalex.org/W2963877580","https://openalex.org/W2963945345","https://openalex.org/W2964073363","https://openalex.org/W2964121507","https://openalex.org/W2964207716","https://openalex.org/W2964262188","https://openalex.org/W2965497096","https://openalex.org/W2969215180","https://openalex.org/W2982569731","https://openalex.org/W3013334753","https://openalex.org/W3021623424","https://openalex.org/W3022125780","https://openalex.org/W3094857757","https://openalex.org/W3099973750","https://openalex.org/W3113425034","https://openalex.org/W3115592686","https://openalex.org/W6639281853","https://openalex.org/W6639384702","https://openalex.org/W6674896736","https://openalex.org/W6677255997","https://openalex.org/W6681017033","https://openalex.org/W6725967330","https://openalex.org/W6739166439","https://openalex.org/W6740380664","https://openalex.org/W6747969630","https://openalex.org/W6748269070","https://openalex.org/W6750531877","https://openalex.org/W6767581218","https://openalex.org/W6773377883","https://openalex.org/W6777674752","https://openalex.org/W6777828934","https://openalex.org/W6781529000","https://openalex.org/W6784843422","https://openalex.org/W6803013564"],"related_works":["https://openalex.org/W2964256664","https://openalex.org/W3118581654","https://openalex.org/W2768927505","https://openalex.org/W3102206315","https://openalex.org/W2969215180","https://openalex.org/W2963099043","https://openalex.org/W2268674159","https://openalex.org/W2140867429","https://openalex.org/W2133105246","https://openalex.org/W2118550318","https://openalex.org/W2106005123","https://openalex.org/W2971195897","https://openalex.org/W2920297477","https://openalex.org/W2948913623","https://openalex.org/W2664571037","https://openalex.org/W2973233842","https://openalex.org/W2951898449","https://openalex.org/W3103820806","https://openalex.org/W2606313559","https://openalex.org/W2933682931"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,38,58,73,88,95,106,125,136,152,159],"problem":[3],"of":[4,90,109,161],"recovering":[5],"low-rank":[6,39],"matrices":[7],"from":[8],"random":[9],"rank-one":[10],"measurements,":[11],"which":[12],"spans":[13],"numerous":[14],"applications":[15],"including":[16],"covariance":[17],"sketching,":[18],"phase":[19],"retrieval,":[20],"quantum":[21],"state":[22],"tomography,":[23],"and":[24,84,124],"learning":[25],"shallow":[26],"polynomial":[27],"neural":[28],"networks,":[29],"among":[30],"others.":[31],"Our":[32],"approach":[33],"is":[34,61,68,94,113],"to":[35,70,72,77,143],"directly":[36],"estimate":[37],"factor":[40],"by":[41,63],"minimizing":[42],"a":[43,53,64,132],"nonconvex":[44],"least-squares":[45],"loss":[46],"function":[47],"via":[48],"vanilla":[49],"gradient":[50,126],"descent,":[51],"following":[52],"tailored":[54],"spectral":[55,122],"initialization.":[56],"When":[57],"true":[59],"rank":[60],"bounded":[62],"constant,":[65],"this":[66,93],"algorithm":[67],"guaranteed":[69],"converge":[71],"ground":[74],"truth":[75],"(up":[76],"global":[78],"ambiguity)":[79],"with":[80,135,151],"near-optimal":[81,110],"sample":[82,162],"complexity":[83],"computational":[85,111],"complexity.":[86],"To":[87],"best":[89],"our":[91],"knowledge,":[92],"first":[96],"guarantee":[97],"that":[98],"achieves":[99],"near-optimality":[100],"in":[101,155],"both":[102,121],"metrics.":[103],"In":[104],"particular,":[105],"key":[107],"enabler":[108],"guarantees":[112],"an":[114],"implicit":[115],"regularization":[116],"phenomenon:":[117],"without":[118,158],"explicit":[119],"regularization,":[120],"initialization":[123],"descent":[127],"iterates":[128],"automatically":[129],"stay":[130],"within":[131],"region":[133],"incoherent":[134],"measurement":[137],"vectors.":[138],"This":[139],"feature":[140],"allows":[141],"one":[142],"employ":[144],"much":[145],"more":[146],"aggressive":[147],"step":[148],"sizes":[149],"compared":[150],"ones":[153],"suggested":[154],"prior":[156],"literature,":[157],"need":[160],"splitting.":[163]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":5}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
