{"id":"https://openalex.org/W2185602187","doi":"https://doi.org/10.48550/arxiv.1412.8729","title":"High Dimensional Expectation-Maximization Algorithm: Statistical Optimization and Asymptotic Normality","display_name":"High Dimensional Expectation-Maximization Algorithm: Statistical Optimization and Asymptotic Normality","publication_year":2014,"publication_date":"2014-12-30","ids":{"openalex":"https://openalex.org/W2185602187","doi":"https://doi.org/10.48550/arxiv.1412.8729","mag":"2185602187","pmid":"https://pubmed.ncbi.nlm.nih.gov/28615917","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/5467221"},"language":"en","primary_location":{"id":"pmid:28615917","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28615917","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,"listed_in":[],"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":"Advances in neural information processing systems","raw_type":"Journal Article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5467221","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101934110","display_name":"Zhaoran Wang","orcid":"https://orcid.org/0000-0002-1824-2580","observed_orcids":["https://orcid.org/0000-0002-1824-2580"]},"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":"Wang, Zhaoran","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/A5051448391","display_name":"Quanquan Gu","orcid":"https://orcid.org/0000-0001-9830-793X","observed_orcids":["https://orcid.org/0000-0001-9830-793X"]},"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":"Gu, Quanquan","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/A5070406375","display_name":"Yang Ning","orcid":"https://orcid.org/0000-0001-6877-9231","observed_orcids":["https://orcid.org/0000-0001-6877-9231"]},"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":"Ning, Yang","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":"last","author":{"id":"https://openalex.org/A5100349057","display_name":"Han Liu","orcid":"https://orcid.org/0000-0002-9386-2464","observed_orcids":["https://orcid.org/0000-0002-9386-2464"]},"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":"Liu, Han","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"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":8.8882,"has_fulltext":true,"cited_by_count":96,"citation_normalized_percentile":{"value":0.98065589,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"28","issue":null,"first_page":"2512","last_page":"2520"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9599999785423279,"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"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9599999785423279,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.029500000178813934,"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"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.0015999999595806003,"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/expectation-maximization-algorithm","display_name":"expectation-maximization algorithm","score":0.9860000014305115},{"id":"https://openalex.org/keywords/sparsity","display_name":"sparsity","score":0.6949999928474426},{"id":"https://openalex.org/keywords/parameter-estimation","display_name":"parameter estimation","score":0.7799999713897705},{"id":"https://openalex.org/keywords/geometric-convergence","display_name":"geometric convergence","score":0.6110000014305115},{"id":"https://openalex.org/keywords/asymptotic-normality","display_name":"asymptotic normality","score":0.8619999885559082},{"id":"https://openalex.org/keywords/hypothesis-testing","display_name":"hypothesis testing","score":0.968999981880188},{"id":"https://openalex.org/keywords/confidence-intervals","display_name":"confidence intervals","score":0.8690000176429749}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6982356309890747},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.6389917135238647},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.6308417320251465},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.6154363751411438},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5469068884849548},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5276809334754944},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5240285992622375},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.5114618539810181},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4694632589817047},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.46882981061935425},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.45518726110458374},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.4512837529182434},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4234566390514374},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4198864996433258},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40751922130584717},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19407185912132263},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.17817869782447815},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15402710437774658},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.14678052067756653},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"pmid:28615917","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28615917","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,"listed_in":[],"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":"Advances in neural information processing systems","raw_type":"Journal Article"},{"id":"pmh:oai:europepmc.org:4316713","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5467221","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:5467221","doi":null,"is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC5467221/","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,"listed_in":[],"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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Adv Neural Inf Process Syst","raw_type":"Text"},{"id":"pmh:oai:arXiv.org:1412.8729","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1412.8729","pdf_url":"https://arxiv.org/pdf/1412.8729","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"doi:10.48550/arxiv.1412.8729","doi":"https://doi.org/10.48550/arxiv.1412.8729","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1412.8729","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"mag:2185602187","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28615917","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,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":"PubMed","raw_type":null}],"best_oa_location":{"id":"pmh:oai:europepmc.org:4316713","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5467221","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1827910668","display_name":"Statistical and Computational Tools for Next-generation ChIP-seq Applications","funder_award_id":"R01HG006841","funder_id":"https://openalex.org/F4320337348","funder_display_name":"National Human Genome Research Institute"},{"id":"https://openalex.org/G3101153843","display_name":"Preprocessing and Analysis Tools for High-Throughput Technologies","funder_award_id":"R01GM083084","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"},{"id":"https://openalex.org/G5785103205","display_name":"Large-Scale Semiparametric Graphical Models with Applications to Neuroscience","funder_award_id":"R01MH102339","funder_id":"https://openalex.org/F4320337346","funder_display_name":"National Institute of Mental Health"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337346","display_name":"National Institute of Mental Health","ror":"https://ror.org/04xeg9z08"},{"id":"https://openalex.org/F4320337348","display_name":"National Human Genome Research Institute","ror":"https://ror.org/00baak391"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2185602187.pdf","grobid_xml":"https://content.openalex.org/works/W2185602187.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W80733463","https://openalex.org/W122168659","https://openalex.org/W403935824","https://openalex.org/W568673721","https://openalex.org/W626711554","https://openalex.org/W1480370952","https://openalex.org/W1535281955","https://openalex.org/W1535995764","https://openalex.org/W1772739125","https://openalex.org/W1812168191","https://openalex.org/W1879772259","https://openalex.org/W1968694834","https://openalex.org/W1989727964","https://openalex.org/W2026523206","https://openalex.org/W2028182876","https://openalex.org/W2046738186","https://openalex.org/W2049633694","https://openalex.org/W2053742104","https://openalex.org/W2069119359","https://openalex.org/W2078411132","https://openalex.org/W2082213488","https://openalex.org/W2105724942","https://openalex.org/W2116581043","https://openalex.org/W2117853077","https://openalex.org/W2119537322","https://openalex.org/W2120846249","https://openalex.org/W2124428910","https://openalex.org/W2131172946","https://openalex.org/W2137404238","https://openalex.org/W2138967244","https://openalex.org/W2146758737","https://openalex.org/W2162636131","https://openalex.org/W2163162137","https://openalex.org/W2171208486","https://openalex.org/W2172185584","https://openalex.org/W2204774351","https://openalex.org/W2401346293","https://openalex.org/W2945109701","https://openalex.org/W2950324686","https://openalex.org/W2952849647","https://openalex.org/W2962737134","https://openalex.org/W2963765119","https://openalex.org/W3003608419","https://openalex.org/W3101651037","https://openalex.org/W3103643510","https://openalex.org/W3141595720","https://openalex.org/W4292494783"],"related_works":["https://openalex.org/W2101522492","https://openalex.org/W7095746464","https://openalex.org/W6996539748","https://openalex.org/W2984280748","https://openalex.org/W2810223212","https://openalex.org/W3098178347","https://openalex.org/W3109792867","https://openalex.org/W3108645401","https://openalex.org/W2593092893","https://openalex.org/W3015299830"],"abstract_inverted_index":{"We":[0],"provide":[1],"a":[2,29,51,92],"general":[3],"theory":[4,116],"of":[5,63,87,95],"the":[6,59,68,101],"expectation-maximization":[7],"(EM)":[8],"algorithm":[9,34,48],"for":[10,76,83,106],"inferring":[11],"high":[12,31,88,113],"dimensional":[13,32,85,89],"latent":[14],"variable":[15],"models.":[16],"In":[17],"particular,":[18],"we":[19,27,71],"make":[20],"two":[21],"contributions:":[22],"(i)":[23],"For":[24,91],"parameter":[25,41],"estimation,":[26],"propose":[28,72],"novel":[30],"EM":[33],"which":[35],"naturally":[36],"incorporates":[37],"sparsity":[38],"structure":[39],"into":[40],"estimation.":[42],"With":[43],"an":[44,56],"appropriate":[45],"initialization,":[46],"this":[47],"converges":[49],"at":[50],"geometric":[52],"rate":[53,62],"and":[54,79,109],"attains":[55],"estimator":[57],"with":[58],"(near-)optimal":[60],"statistical":[61,96],"convergence.":[64],"(ii)":[65],"Based":[66],"on":[67],"obtained":[69],"estimator,":[70],"new":[73],"inferential":[74],"procedures":[75],"testing":[77],"hypotheses":[78],"constructing":[80],"confidence":[81],"intervals":[82],"low":[84],"components":[86],"parameters.":[90],"broad":[93],"family":[94],"models,":[97],"our":[98],"framework":[99],"establishes":[100],"first":[102],"computationally":[103],"feasible":[104],"approach":[105],"optimal":[107],"estimation":[108],"asymptotic":[110],"inference":[111],"in":[112],"dimensions.":[114],"Our":[115],"is":[117],"supported":[118],"by":[119],"thorough":[120],"numerical":[121],"results.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":7}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2016-06-24T00:00:00"}
