{"id":"https://openalex.org/W2963799966","doi":"https://doi.org/10.1109/isit.2018.8437725","title":"Minimax Optimal Additive Functional Estimation with Discrete Distribution: Slow Divergence Speed Case","display_name":"Minimax Optimal Additive Functional Estimation with Discrete Distribution: Slow Divergence Speed Case","publication_year":2018,"publication_date":"2018-06-01","ids":{"openalex":"https://openalex.org/W2963799966","doi":"https://doi.org/10.1109/isit.2018.8437725","mag":"2963799966"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2018.8437725","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2018.8437725","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008914720","display_name":"Kazuto Fukuchi","orcid":"https://orcid.org/0000-0003-3895-219X"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]},{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuto Fukuchi","raw_affiliation_strings":["15th floor, 1-4-1 Nihonbashi, RIKEN Center for Advanced Intelligence Project Nihonbashi 1-chome Mitsui Building, Chuo-ku, Tokyo, 103-0027, Japan","Department of Computer Science, Graduate School of SIE University of Tsukuba, Gobancho, Chiyoda-ku, Tokyo, Ibaraki, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"15th floor, 1-4-1 Nihonbashi, RIKEN Center for Advanced Intelligence Project Nihonbashi 1-chome Mitsui Building, Chuo-ku, Tokyo, 103-0027, Japan","institution_ids":["https://openalex.org/I4210126580"]},{"raw_affiliation_string":"Department of Computer Science, Graduate School of SIE University of Tsukuba, Gobancho, Chiyoda-ku, Tokyo, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022139141","display_name":"Jun Sakuma","orcid":"https://orcid.org/0000-0001-5015-3812"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Jun Sakuma","raw_affiliation_strings":["Graduate School of SIE University of Tsukuba, 1-1-1 Tennodai, Department of Computer Science, Tsukuba, Ibaraki, 305-8577, Japan","Department of Computer Science, Graduate School of SIE University of Tsukuba, Gobancho, Chiyoda-ku, Tokyo, Ibaraki, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of SIE University of Tsukuba, 1-1-1 Tennodai, Department of Computer Science, Tsukuba, Ibaraki, 305-8577, Japan","institution_ids":["https://openalex.org/I146399215"]},{"raw_affiliation_string":"Department of Computer Science, Graduate School of SIE University of Tsukuba, Gobancho, Chiyoda-ku, Tokyo, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1041","last_page":"1045"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9958000183105469,"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"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9958000183105469,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9930999875068665,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9908000230789185,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.6262036561965942},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5313504338264465},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.49520984292030334},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.44296756386756897},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.43143588304519653},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41561904549598694},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41040733456611633},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38124725222587585},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35848772525787354},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.31430453062057495},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19933035969734192},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1366281807422638},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.08994755148887634}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.6262036561965942},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5313504338264465},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.49520984292030334},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.44296756386756897},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.43143588304519653},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41561904549598694},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41040733456611633},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38124725222587585},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35848772525787354},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31430453062057495},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19933035969734192},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1366281807422638},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.08994755148887634},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2018.8437725","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2018.8437725","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3829070172","display_name":"Statistical Security of Machine Learning","funder_award_id":"16H02864","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320338075","display_name":"Core Research for Evolutional Science and Technology","ror":"https://ror.org/00097mb19"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W68584319","https://openalex.org/W81138975","https://openalex.org/W568673721","https://openalex.org/W1488107580","https://openalex.org/W1535258871","https://openalex.org/W1989151402","https://openalex.org/W2030562249","https://openalex.org/W2058815839","https://openalex.org/W2148719904","https://openalex.org/W2314477198","https://openalex.org/W2581645951","https://openalex.org/W2950286539","https://openalex.org/W2963017284","https://openalex.org/W2963608890","https://openalex.org/W2963694441","https://openalex.org/W2963720577","https://openalex.org/W3101382006","https://openalex.org/W4214577758","https://openalex.org/W4245577611","https://openalex.org/W6629061337"],"related_works":["https://openalex.org/W2105321464","https://openalex.org/W2887774187","https://openalex.org/W2388220555","https://openalex.org/W1554844486","https://openalex.org/W1520875569","https://openalex.org/W3048739257","https://openalex.org/W1665563134","https://openalex.org/W2963604926","https://openalex.org/W2199957582","https://openalex.org/W2033178790"],"abstract_inverted_index":{"This":[0],"paper":[1,68],"addresses":[2],"a":[3,16,52,111,128],"problem":[4,77],"of":[5,59,75,99,115],"estimating":[6],"an":[7],"additive":[8,34],"functional":[9,35],"given":[10],"n":[11],"i.i.d.":[12],"samples":[13],"drawn":[14],"from":[15],"discrete":[17],"distribution":[18],"P=(p":[19],"<sub":[20,25,40,47],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[21,26,41,44,48,147,151],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[22],",":[23],"...,p":[24],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</sub>":[27],")":[28,50],"with":[29],"alphabet":[30],"size":[31],"k.":[32],"The":[33],"is":[36,78,87],"defined":[37],"as":[38],"\u03b8(P;\u03c6)=\u03a3":[39],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i=1</sub>":[42],"<sup":[43,146,150],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</sup>":[45],"\u03c6(p":[46],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i</sub>":[49],"for":[51,136],"function":[53],"\u03c6,":[54],"which":[55],"covers":[56],"the":[57,60,66,71,81,85,97,100,116,133],"most":[58],"entropy-like":[61],"criteria.":[62],"We":[63],"revealed":[64],"in":[65],"previous":[67],"[1]":[69],"that":[70,132],"minimax":[72,134],"optimal":[73],"rate":[74],"this":[76,104,108],"characterized":[79],"by":[80],"divergence":[82,101,117],"speed,":[83,118],"whereas":[84],"characterization":[86,109],"valid":[88],"only":[89],"when":[90],"\u03b1":[91,95,120,124,137,141],"\u2208":[92,121,125,138,142],"(0,1)":[93],"where":[94],"denotes":[96],"parameter":[98],"speed.":[102],"In":[103],"paper,":[105],"we":[106,130],"extend":[107],"to":[110],"more":[112],"general":[113],"range":[114],"including":[119],"(1,3/2)":[122,139],"and":[123,140,154],"[3/2,2].":[126],"As":[127],"result,":[129],"show":[131],"rates":[135],"[3/2,2]":[143],"are":[144],"[1/n]+[(k":[145],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[148],")/((nlnn)":[149],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2\u03b1</sup>":[152],")]":[153],"[1/n],":[155],"respectively.":[156]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}