{"id":"https://openalex.org/W2148719904","doi":"https://doi.org/10.1109/tit.2017.2733537","title":"Maximum Likelihood Estimation of Functionals of Discrete Distributions","display_name":"Maximum Likelihood Estimation of Functionals of Discrete Distributions","publication_year":2017,"publication_date":"2017-07-31","ids":{"openalex":"https://openalex.org/W2148719904","doi":"https://doi.org/10.1109/tit.2017.2733537","mag":"2148719904"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2733537","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2733537","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"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1406.6959","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034192173","display_name":"Jiantao Jiao","orcid":"https://orcid.org/0000-0003-3766-8031"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jiantao Jiao","raw_affiliation_strings":["Department of Electrical Engineering, Stanford University, Stanford, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066970557","display_name":"Kartik Venkat","orcid":"https://orcid.org/0000-0002-7902-9724"},"institutions":[{"id":"https://openalex.org/I4210097638","display_name":"Partners In Care","ror":"https://ror.org/00xwb4n23","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210097638"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kartik Venkat","raw_affiliation_strings":["Department of Electrical Engineering, Stanford University, Stanford, CA, USA","PDT Partners, New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"PDT Partners, New York, NY, USA","institution_ids":["https://openalex.org/I4210097638"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077972639","display_name":"Yanjun Han","orcid":"https://orcid.org/0000-0002-8335-2364"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yanjun Han","raw_affiliation_strings":["Department of Electrical Engineering, Stanford University, Stanford, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043344688","display_name":"Tsachy Weissman","orcid":"https://orcid.org/0009-0008-1099-691X"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tsachy Weissman","raw_affiliation_strings":["Department of Electrical Engineering, Stanford University, Stanford, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5034192173"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":16.2738,"has_fulltext":true,"cited_by_count":108,"citation_normalized_percentile":{"value":0.9951663,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"63","issue":"10","first_page":"6774","last_page":"6798"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9883999824523926,"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":0.9883999824523926,"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":0.9811000227928162,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9690999984741211,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7859381437301636},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7369201183319092},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.687799334526062},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.682003378868103},{"id":"https://openalex.org/keywords/minimax-estimator","display_name":"Minimax estimator","score":0.6292779445648193},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5726602077484131},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.49860453605651855},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.4433688223361969},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.43104618787765503},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.42429155111312866},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.35826361179351807},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2879191040992737},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.2592725157737732},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1548994779586792}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7859381437301636},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7369201183319092},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.687799334526062},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.682003378868103},{"id":"https://openalex.org/C133939421","wikidata":"https://www.wikidata.org/wiki/Q6865379","display_name":"Minimax estimator","level":4,"score":0.6292779445648193},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5726602077484131},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.49860453605651855},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4433688223361969},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.43104618787765503},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.42429155111312866},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.35826361179351807},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2879191040992737},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.2592725157737732},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1548994779586792},{"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/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2017.2733537","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2733537","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:1406.6959","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1406.6959","pdf_url":"https://arxiv.org/pdf/1406.6959","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":null,"raw_type":"text"},{"id":"pmh:oai:arXiv.org:1502.00327","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1502.00327","pdf_url":"https://arxiv.org/pdf/1502.00327","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1406.6959","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1406.6959","pdf_url":"https://arxiv.org/pdf/1406.6959","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":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.550000011920929,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":92,"referenced_works":["https://openalex.org/W568673721","https://openalex.org/W579420740","https://openalex.org/W608637647","https://openalex.org/W1488107580","https://openalex.org/W1488909131","https://openalex.org/W1507943102","https://openalex.org/W1511694993","https://openalex.org/W1516339661","https://openalex.org/W1533375765","https://openalex.org/W1535258871","https://openalex.org/W1568559199","https://openalex.org/W1603339577","https://openalex.org/W1635484243","https://openalex.org/W1661915592","https://openalex.org/W1732328119","https://openalex.org/W1856858227","https://openalex.org/W1874027545","https://openalex.org/W1966695467","https://openalex.org/W1967436950","https://openalex.org/W1971405816","https://openalex.org/W1982918157","https://openalex.org/W1988510005","https://openalex.org/W1989151402","https://openalex.org/W1989164662","https://openalex.org/W1992068214","https://openalex.org/W1992536060","https://openalex.org/W1995875735","https://openalex.org/W2000163531","https://openalex.org/W2006714754","https://openalex.org/W2008551287","https://openalex.org/W2018891628","https://openalex.org/W2022825068","https://openalex.org/W2023112529","https://openalex.org/W2026664846","https://openalex.org/W2026781197","https://openalex.org/W2045114504","https://openalex.org/W2046495522","https://openalex.org/W2055403763","https://openalex.org/W2059584073","https://openalex.org/W2067883080","https://openalex.org/W2072302731","https://openalex.org/W2079517420","https://openalex.org/W2097173970","https://openalex.org/W2097636360","https://openalex.org/W2101985079","https://openalex.org/W2109647515","https://openalex.org/W2114771311","https://openalex.org/W2117897510","https://openalex.org/W2122401230","https://openalex.org/W2122882636","https://openalex.org/W2124055802","https://openalex.org/W2125232050","https://openalex.org/W2127090196","https://openalex.org/W2135191607","https://openalex.org/W2137601763","https://openalex.org/W2145267250","https://openalex.org/W2156875677","https://openalex.org/W2312228542","https://openalex.org/W2330820318","https://openalex.org/W2406099650","https://openalex.org/W2474885752","https://openalex.org/W2478708596","https://openalex.org/W2510474575","https://openalex.org/W2518306676","https://openalex.org/W2550177130","https://openalex.org/W2554091414","https://openalex.org/W2561586961","https://openalex.org/W2567030849","https://openalex.org/W2594457276","https://openalex.org/W2736230390","https://openalex.org/W2752921537","https://openalex.org/W2899702797","https://openalex.org/W2963389257","https://openalex.org/W2963608890","https://openalex.org/W2963970827","https://openalex.org/W2993383518","https://openalex.org/W3100848448","https://openalex.org/W4205354563","https://openalex.org/W4230173782","https://openalex.org/W4235461144","https://openalex.org/W4242237682","https://openalex.org/W4245378867","https://openalex.org/W4245577611","https://openalex.org/W4247267886","https://openalex.org/W4299432846","https://openalex.org/W4302561155","https://openalex.org/W6670265044","https://openalex.org/W6674669923","https://openalex.org/W6676307221","https://openalex.org/W6678263215","https://openalex.org/W6740917271","https://openalex.org/W6891767880"],"related_works":["https://openalex.org/W3174947331","https://openalex.org/W237619808","https://openalex.org/W2104713681","https://openalex.org/W2895916002","https://openalex.org/W2034921015","https://openalex.org/W2045096965","https://openalex.org/W3021846434","https://openalex.org/W35332197","https://openalex.org/W2072918764","https://openalex.org/W2064875109"],"abstract_inverted_index":{"We":[0,37,75,384],"consider":[1,207],"the":[2,27,43,53,63,69,78,86,93,116,165,191,216,254,271,280,292,309,312,322,329,334,351,357,361,367,373,381,395,404,407,414,423],"problem":[3],"of":[4,7,26,33,46,55,65,277,321,328,422,438],"estimating":[5,92],"functionals":[6],"discrete":[8],"distributions,":[9],"and":[10,52,115,159,182,204,242],"focus":[11],"on":[12],"a":[13,170,257],"tight":[14],"(up":[15],"to":[16,41,61,144,184,193,206,218,349,365],"universal":[17,145],"multiplicative":[18,146],"constants":[19,147],"for":[20,148,152,163,172,190,215,235,279,287,339,370,376],"each":[21,149],"specific":[22],"functional)":[23],"nonasymptotic":[24],"analysis":[25],"worst":[28,79,272],"case":[29,80,273],"squared":[30,81,274,294,377],"error":[31,82,275,295],"risk":[32,83,166],"widely":[34],"used":[35],"estimators.":[36],"apply":[38],"concentration":[39],"inequalities":[40],"analyze":[42,62,333],"random":[44],"fluctuation":[45],"these":[47],"estimators":[48,234,390,442],"around":[49],"their":[50,66,73],"expectations":[51,67],"theory":[54],"approximation":[56],"using":[57],"positive":[58],"linear":[59],"operators":[60],"deviation":[64],"from":[68],"true":[70],"functional,":[71,151,359],"namely":[72],"bias.":[74],"explicitly":[76],"characterize":[77],"incurred":[84],"by":[85],"maximum":[87,396],"likelihood":[88,397],"estimator":[89,369,426],"(MLE)":[90],"in":[91,387,406,417],"Shannon":[94,173,340],"entropy":[95,174,341,358,371,418,441],"H(P)":[96],"=":[97,124],"\u03a3":[98,125],"<sub":[99,106,111,120,126,133,222],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[100,103,107,112,121,127,130,134,137,212,223,245,285,302,318],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i=1</sub>":[101,128],"<sup":[102,129,136,211,244,284,301,317],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">S</sup>":[104,131],"-p":[105],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i</sub>":[108,113,135],"ln":[109,240,248,299,445],"p":[110,132],",":[114,139],"power":[117],"sum":[118],"F":[119,221],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b1</sub>":[122,224],"(P)":[123],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b1</sup>":[138],"\u03b1":[140,228,265,306],">":[141],"0,":[142],"up":[143],"fixed":[150],"any":[153],"alphabet":[154,289,323],"size":[155,161],"S":[156,188,210,241,243,249],"\u2264":[157],"\u221e":[158],"sample":[160,260],"n":[162,186,208,283,316,428,444,446],"which":[164,251,379],"may":[167],"vanish.":[168],"As":[169,325],"corollary,":[171],"estimation,":[175],"we":[176,198,268,332,402],"show":[177,269,385],"that":[178,200,253,270,386,437],"it":[179,201],"is":[180,202,282,297,348,364,380,430],"necessary":[181,203],"sufficient":[183,205],"have":[185],"\u226b":[187,209],"observations":[189],"MLE":[192,217,255,281,310],"be":[194],"consistent.":[195],"In":[196,343],"addition,":[197],"establish":[199],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1/\u03b1</sup>":[213,246],"samples":[214,429],"consistently":[219],"estimate":[220],"(P),":[225],"0":[226],"<;":[227,229,264,266],"1.":[230],"The":[231,420],"minimax":[232,293,313,415,424],"rate-optimal":[233,425],"both":[236],"problems":[237],"require":[238],"S/":[239],"/":[247],"samples,":[250],"implies":[252],"has":[256],"strictly":[258],"sub-optimal":[259],"complexity.":[261],"When":[262,305],"1":[263],"3/2,":[267,308],"rate":[276,296,315],"convergence":[278],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-2(\u03b1-1)</sup>":[286,303],"infinite":[288],"size,":[290],"while":[291,360],"(n":[298],"n)":[300],".":[304],"\u2265":[307],"achieves":[311],"optimal":[314],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-1</sup>":[319],"regardless":[320],"size.":[324],"an":[326],"application":[327],"general":[330,388],"theory,":[331],"Dirichlet":[335,352,374,408,439],"prior":[336,353,375],"smoothing":[337],"techniques":[338],"estimation.":[342,419],"this":[344,410],"context,":[345],"one":[346,363],"approach":[347,411],"plug-in":[350],"smoothed":[354,440],"distribution":[355],"into":[356],"other":[362],"calculate":[366],"Bayes":[368],"under":[372],"error,":[378],"conditional":[382],"expectation.":[383],"such":[389],"do":[391],"not":[392],"improve":[393],"over":[394],"estimator.":[398],"No":[399],"matter":[400],"how":[401],"tune":[403],"parameters":[405],"prior,":[409],"cannot":[412],"achieve":[413],"rates":[416],"performance":[421],"with":[427,443],"essentially":[431],"at":[432],"least":[433],"as":[434,436],"good":[435],"samples.":[447]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":26},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":8}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
