{"id":"https://openalex.org/W2183157416","doi":null,"title":"Non-convex Statistical Optimization for Sparse Tensor Graphical Model.","display_name":"Non-convex Statistical Optimization for Sparse Tensor Graphical Model.","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2183157416","mag":"2183157416","pmid":"https://pubmed.ncbi.nlm.nih.gov/28316459","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/5354362"},"language":"en","primary_location":{"id":"pmid:28316459","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28316459","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":["pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5354362","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086153438","display_name":"Wei Sun","orcid":"https://orcid.org/0000-0002-6350-1107","observed_orcids":["https://orcid.org/0000-0002-6350-1107"]},"institutions":[{"id":"https://openalex.org/I4210134091","display_name":"Yahoo (United States)","ror":"https://ror.org/040dkzz12","country_code":"US","type":"company","lineage":["https://openalex.org/I4210134091"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wei Sun","raw_affiliation_strings":["Yahoo Labs, Sunnyvale, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yahoo Labs, Sunnyvale, CA","institution_ids":["https://openalex.org/I4210134091"]}]},{"author_position":"middle","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":"Zhaoran Wang","raw_affiliation_strings":["Department of Operations Research, and Financial Engineering, Princeton University, Princeton, NJ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Operations Research, and Financial Engineering, Princeton University, Princeton, NJ","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","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":"Han Liu","raw_affiliation_strings":["Department of Operations Research, and Financial Engineering, Princeton University, Princeton, NJ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Operations Research, and Financial Engineering, Princeton University, Princeton, NJ","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101688179","display_name":"Guang Cheng","orcid":"https://orcid.org/0000-0002-7874-9404","observed_orcids":["https://orcid.org/0000-0002-7874-9404"]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guang Cheng","raw_affiliation_strings":["Department of Statistics, Purdue University, West Lafayette, IN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Purdue University, West Lafayette, IN","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7579,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.80508275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"28","issue":null,"first_page":"1081","last_page":"1089"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9564999938011169,"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":0.9564999938011169,"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/T12303","display_name":"Tensor decomposition and applications","score":0.04100000113248825,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.0003000000142492354,"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/sparse-graphical-models","display_name":"sparse graphical models","score":0.9100000262260437},{"id":"https://openalex.org/keywords/precision-matrix-estimation","display_name":"precision matrix estimation","score":0.8330000042915344},{"id":"https://openalex.org/keywords/kronecker-product-covariance-structure","display_name":"Kronecker product covariance structure","score":0.8579999804496765},{"id":"https://openalex.org/keywords/nonconvex-optimization","display_name":"non-convex optimization","score":0.9359999895095825},{"id":"https://openalex.org/keywords/penalized-likelihood","display_name":"penalized likelihood","score":0.9169999957084656},{"id":"https://openalex.org/keywords/alternating-optimization","display_name":"alternating optimization","score":0.9269999861717224},{"id":"https://openalex.org/keywords/graph-recovery","display_name":"graph recovery","score":0.593999981880188},{"id":"https://openalex.org/keywords/high-dimensional-statistics","display_name":"high-dimensional statistics","score":0.6840000152587891},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.6100000143051147}],"concepts":[{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.7384573221206665},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6876510977745056},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5824949741363525},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5391882061958313},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.48167550563812256},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4689328968524933},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46811121702194214},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4382658004760742},{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.4157227873802185},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4135245680809021},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40363389253616333},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.27044808864593506},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13365012407302856},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmid:28316459","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28316459","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:pubmedcentral.nih.gov:5354362","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5354362","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:CiteSeerX.psu:10.1.1.699.7018","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.699.7018","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stat.purdue.edu/%7Echengg/Tlasso_nips2015.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.726.5003","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.726.5003","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.princeton.edu/%7Ezhaoran/papers/STGM.pdf","raw_type":"text"},{"id":"mag:2183157416","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28316459","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:pubmedcentral.nih.gov:5354362","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5354362","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"},"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/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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W98990758","https://openalex.org/W301343586","https://openalex.org/W331379265","https://openalex.org/W1862068047","https://openalex.org/W1963482188","https://openalex.org/W1974105260","https://openalex.org/W1980067858","https://openalex.org/W2024165284","https://openalex.org/W2039954784","https://openalex.org/W2049459260","https://openalex.org/W2066986830","https://openalex.org/W2068943743","https://openalex.org/W2069049877","https://openalex.org/W2081746825","https://openalex.org/W2086400086","https://openalex.org/W2089349245","https://openalex.org/W2095640740","https://openalex.org/W2097581234","https://openalex.org/W2105459687","https://openalex.org/W2105724942","https://openalex.org/W2106005123","https://openalex.org/W2125156589","https://openalex.org/W2131668296","https://openalex.org/W2132555912","https://openalex.org/W2135046866","https://openalex.org/W2150940164","https://openalex.org/W2158746276","https://openalex.org/W2293082389","https://openalex.org/W2406138340","https://openalex.org/W2586353914","https://openalex.org/W2963774180","https://openalex.org/W3006275134","https://openalex.org/W3103368540","https://openalex.org/W3148198191","https://openalex.org/W4301425558"],"related_works":["https://openalex.org/W2963246011","https://openalex.org/W2049459260","https://openalex.org/W4362643489","https://openalex.org/W4401692047","https://openalex.org/W3166296073","https://openalex.org/W4297469848","https://openalex.org/W2612480691","https://openalex.org/W2622480976","https://openalex.org/W2905281319","https://openalex.org/W2989402453"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,10,19,22,30,34,65,87,93],"estimation":[3,20,52,69,110],"of":[4,13,21,29,53,64,67,97],"sparse":[5,82],"graphical":[6],"models":[7],"that":[8,73],"characterize":[9],"dependency":[11],"structure":[12],"high-dimensional":[14],"tensor-valued":[15],"data.":[16],"To":[17],"facilitate":[18],"precision":[23,83],"matrix":[24,84],"corresponding":[25],"to":[26],"each":[27,81],"way":[28],"tensor,":[31],"we":[32,71],"assume":[33],"data":[35],"follow":[36],"a":[37,44,58],"tensor":[38,115],"normal":[39],"distribution":[40],"whose":[41],"covariance":[42],"has":[43],"Kronecker":[45],"product":[46],"structure.":[47],"The":[48],"penalized":[49],"maximum":[50],"likelihood":[51],"this":[54,68],"model":[55],"involves":[56],"minimizing":[57],"non-convex":[59],"objective":[60],"function.":[61],"In":[62],"spite":[63],"non-convexity":[66],"problem,":[70],"prove":[72],"an":[74,90,107],"alternating":[75],"minimization":[76],"algorithm,":[77],"which":[78,117],"iteratively":[79],"estimates":[80],"while":[85],"fixing":[86],"others,":[88],"attains":[89],"estimator":[91,108],"with":[92,112],"optimal":[94],"statistical":[95],"rate":[96],"convergence":[98],"as":[99,101],"well":[100],"consistent":[102],"graph":[103],"recovery.":[104],"Notably,":[105],"such":[106],"achieves":[109],"consistency":[111],"only":[113],"one":[114],"sample,":[116],"is":[118],"unobserved":[119],"in":[120],"previous":[121],"work.":[122],"Our":[123],"theoretical":[124],"results":[125],"are":[126],"backed":[127],"by":[128],"thorough":[129],"numerical":[130],"studies.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
