{"id":"https://openalex.org/W1601475477","doi":"https://doi.org/10.1109/ijcnn.2005.1556038","title":"An optimal entropy estimator for discrete random variables","display_name":"An optimal entropy estimator for discrete random variables","publication_year":2006,"publication_date":"2006-01-05","ids":{"openalex":"https://openalex.org/W1601475477","doi":"https://doi.org/10.1109/ijcnn.2005.1556038","mag":"1601475477"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2005.1556038","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2005.1556038","pdf_url":null,"source":{"id":"https://openalex.org/S4363609022","display_name":"Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005.","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005.","raw_type":"proceedings-article"},"type":"article","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/A5083977312","display_name":"M. Shiga","orcid":"https://orcid.org/0000-0003-2434-4716"},"institutions":[{"id":"https://openalex.org/I42405503","display_name":"Gifu University","ror":"https://ror.org/024exxj48","country_code":"JP","type":"education","lineage":["https://openalex.org/I42405503"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"M. Shiga","raw_affiliation_strings":["Graduate School of Engineering, Gifu University, Gifu, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Engineering, Gifu University, Gifu, Japan","institution_ids":["https://openalex.org/I42405503"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112581911","display_name":"Y. Yokota","orcid":null},"institutions":[{"id":"https://openalex.org/I42405503","display_name":"Gifu University","ror":"https://ror.org/024exxj48","country_code":"JP","type":"education","lineage":["https://openalex.org/I42405503"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Y. Yokota","raw_affiliation_strings":["Department of Information Science, Faculty of Engineering, Gifu University, Gifu, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Information Science, Faculty of Engineering, Gifu University, Gifu, Japan","institution_ids":["https://openalex.org/I42405503"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083977312"],"corresponding_institution_ids":["https://openalex.org/I42405503"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.06603774,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"2","issue":null,"first_page":"1280","last_page":"1285"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11236","display_name":"Control Systems and Identification","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9872999787330627,"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":0.9871000051498413,"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/estimator","display_name":"Estimator","score":0.8439069986343384},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.8333380222320557},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7344347238540649},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.6224075555801392},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5440144538879395},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5267552733421326},{"id":"https://openalex.org/keywords/entropy-estimation","display_name":"Entropy estimation","score":0.5115838646888733},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4823414981365204},{"id":"https://openalex.org/keywords/bias-of-an-estimator","display_name":"Bias of an estimator","score":0.47290146350860596},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.46224379539489746},{"id":"https://openalex.org/keywords/minimax-estimator","display_name":"Minimax estimator","score":0.41814762353897095},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.23595738410949707}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8439069986343384},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.8333380222320557},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7344347238540649},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.6224075555801392},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5440144538879395},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5267552733421326},{"id":"https://openalex.org/C95546049","wikidata":"https://www.wikidata.org/wiki/Q1345207","display_name":"Entropy estimation","level":3,"score":0.5115838646888733},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4823414981365204},{"id":"https://openalex.org/C191393472","wikidata":"https://www.wikidata.org/wiki/Q15222032","display_name":"Bias of an estimator","level":4,"score":0.47290146350860596},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.46224379539489746},{"id":"https://openalex.org/C133939421","wikidata":"https://www.wikidata.org/wiki/Q6865379","display_name":"Minimax estimator","level":4,"score":0.41814762353897095},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.23595738410949707},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ijcnn.2005.1556038","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2005.1556038","pdf_url":null,"source":{"id":"https://openalex.org/S4363609022","display_name":"Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005.","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1594210692","https://openalex.org/W1992536060","https://openalex.org/W2114771311","https://openalex.org/W2117509237","https://openalex.org/W2151387592"],"related_works":["https://openalex.org/W2034921015","https://openalex.org/W59993211","https://openalex.org/W2889261288","https://openalex.org/W2064875109","https://openalex.org/W4385752617","https://openalex.org/W4220863428","https://openalex.org/W2138355589","https://openalex.org/W1607067789","https://openalex.org/W2037392957","https://openalex.org/W1970204180"],"abstract_inverted_index":{"This":[0],"paper":[1,51],"presents":[2,52],"analytical":[3],"formulations":[4],"of":[5,22,29,35,63,74,132],"the":[6,20,64,67,75,89],"most":[7],"important":[8,41],"estimation":[9,121],"errors-averaged":[10],"squared":[11,16,61,71,97],"bias":[12,72],"error":[13,17,62,73,98],"and":[14,135],"mean":[15,60,96,110],"-":[18],"for":[19,116,125],"class":[21,34],"entropy":[23,36,42,55,91,101,104,113],"estimator":[24,37,56,92],"expressed":[25],"as":[26,107],"a":[27,94],"sum":[28],"single":[30],"variable":[31],"functions.":[32],"The":[33],"includes":[38],"almost":[39],"all":[40],"estimators":[43,102],"that":[44,57,69,88],"have":[45],"been":[46],"proposed":[47,90],"heretofore.":[48],"Furthermore,":[49],"this":[50],"an":[53,81,108],"optimal":[54],"can":[58],"minimize":[59],"estimate":[65,76],"under":[66],"condition":[68],"averaged":[70],"is":[77,105,122],"restricted":[78],"to":[79],"below":[80],"arbitrary":[82],"value.":[83],"A":[84],"numerical":[85],"experiment":[86],"demonstrates":[87],"provides":[93],"lower":[95],"than":[99],"conventional":[100],"when":[103],"estimated":[106],"ensemble":[109],"over":[111],"plural":[112],"estimates":[114],"obtained":[115],"different":[117],"independent":[118],"data.":[119],"Such":[120],"often":[123],"utilized":[124],"biological":[126,133],"signals,":[127,130],"e.g.,":[128],"neural":[129],"because":[131],"tiredness":[134],"adaptation":[136],"property.":[137]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}