{"id":"https://openalex.org/W7147508484","doi":"https://doi.org/10.48550/arxiv.2603.28346","title":"Machine Learning-Assisted High-Dimensional Matrix Estimation","display_name":"Machine Learning-Assisted High-Dimensional Matrix Estimation","publication_year":2026,"publication_date":"2026-03-30","ids":{"openalex":"https://openalex.org/W7147508484","doi":"https://doi.org/10.48550/arxiv.2603.28346"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.28346","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28346","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.28346","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128486202","display_name":"Wan Tian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tian, Wan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132612812","display_name":"Hui Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Hui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114425298","display_name":"Zhouhui Lian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lian, Zhouhui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132583955","display_name":"Lingyue Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Lingyue","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5132691707","display_name":"Yijie Peng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peng, Yijie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.5440999865531921,"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":0.5440999865531921,"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.16030000150203705,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.10639999806880951,"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/estimator","display_name":"Estimator","score":0.6510999798774719},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6471999883651733},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.4805999994277954},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.46059998869895935},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4320000112056732},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4262999892234802},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.40529999136924744},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3522000014781952}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6510999798774719},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6471999883651733},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6154999732971191},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4848000109195709},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.4805999994277954},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.46059998869895935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44530001282691956},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4320000112056732},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42820000648498535},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4262999892234802},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.40529999136924744},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3522000014781952},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.35019999742507935},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3314000070095062},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C31388003","wikidata":"https://www.wikidata.org/wiki/Q7624548","display_name":"Strong consistency","level":3,"score":0.32510000467300415},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3091999888420105},{"id":"https://openalex.org/C205555498","wikidata":"https://www.wikidata.org/wiki/Q505588","display_name":"CMA-ES","level":4,"score":0.28929999470710754},{"id":"https://openalex.org/C39425265","wikidata":"https://www.wikidata.org/wiki/Q7098944","display_name":"Optimal estimation","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.27880001068115234},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.26820001006126404},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2524999976158142}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.28346","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28346","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":"doi:10.48550/arxiv.2603.28346","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28346","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Efficient":[0],"estimation":[1,60,109,158],"of":[2,11,25,70,87,120,131,159,170,186],"high-dimensional":[3,40,58,71,161,187],"matrices-including":[4],"covariance":[5,162],"and":[6,30,95,111,122,129,152,163,184],"precision":[7,164],"matrices-is":[8],"a":[9,77,143],"cornerstone":[10],"modern":[12],"multivariate":[13],"statistics.":[14],"Most":[15],"existing":[16],"studies":[17],"have":[18],"focused":[19],"primarily":[20],"on":[21,81],"the":[22,26,35,67,82,97,101,118,125,139,148,157,168],"theoretical":[23],"properties":[24],"estimators":[27],"(e.g.,":[28],"consistency":[29],"sparsity),":[31],"while":[32],"largely":[33],"overlooking":[34],"computational":[36],"challenges":[37],"inherent":[38],"in":[39,46,100],"settings.":[41],"Motivated":[42],"by":[43,62,173],"recent":[44],"advances":[45],"learning-based":[47],"optimization":[48,55,68,179],"method-which":[49],"integrate":[50],"data-driven":[51],"structures":[52,183],"with":[53,104,176],"classical":[54,178],"algorithms-we":[56],"explore":[57],"matrix":[59,72],"assisted":[61],"machine":[63],"learning.":[64],"Specifically,":[65],"for":[66],"problem":[69],"estimation,":[73],"we":[74,115,136],"first":[75,116],"present":[76],"solution":[78],"procedure":[79],"based":[80],"Linearized":[83],"Alternating":[84],"Direction":[85],"Method":[86],"Multipliers":[88],"(LADMM).":[89],"We":[90,166],"then":[91,123],"introduce":[92],"learnable":[93],"parameters":[94],"model":[96],"proximal":[98],"operators":[99],"iterative":[102],"scheme":[103],"neural":[105],"networks,":[106],"thereby":[107],"improving":[108],"accuracy":[110],"accelerating":[112],"convergence.":[113],"Theoretically,":[114],"prove":[117],"convergence":[119,127,145],"LADMM,":[121],"establish":[124],"convergence,":[126],"rate,":[128],"monotonicity":[130],"its":[132],"reparameterized":[133,140],"counterpart;":[134],"importantly,":[135],"show":[137],"that":[138],"LADMM":[141],"enjoys":[142],"faster":[144],"rate.":[146],"Notably,":[147],"proposed":[149],"reparameterization":[150],"theory":[151],"methodology":[153],"are":[154],"applicable":[155],"to":[156],"both":[160],"matrices.":[165,188],"validate":[167],"effectiveness":[169],"our":[171],"method":[172],"comparing":[174],"it":[175],"several":[177],"algorithms":[180],"across":[181],"different":[182],"dimensions":[185]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-02T00:00:00"}