{"id":"https://openalex.org/W1975526799","doi":"https://doi.org/10.1109/isit.2012.6283012","title":"Estimation of the entropy on the basis of its polynomial representation","display_name":"Estimation of the entropy on the basis of its polynomial representation","publication_year":2012,"publication_date":"2012-07-01","ids":{"openalex":"https://openalex.org/W1975526799","doi":"https://doi.org/10.1109/isit.2012.6283012","mag":"1975526799"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2012.6283012","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6283012","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","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/A5033216984","display_name":"Martin Vinck","orcid":"https://orcid.org/0000-0002-4044-0970"},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]},{"id":"https://openalex.org/I4210108594","display_name":"Amsterdam Neuroscience","ror":"https://ror.org/01x2d9f70","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210108594"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Martin Vinck","raw_affiliation_strings":["Center for Neuroscience, University of Amsterdam, Amsterdam, Netherlands","Center for Neuroscience, University of Amsterdam, Amsterdam, The Netherlands, 1098 XH"],"affiliations":[{"raw_affiliation_string":"Center for Neuroscience, University of Amsterdam, Amsterdam, Netherlands","institution_ids":["https://openalex.org/I4210108594","https://openalex.org/I887064364"]},{"raw_affiliation_string":"Center for Neuroscience, University of Amsterdam, Amsterdam, The Netherlands, 1098 XH","institution_ids":["https://openalex.org/I887064364"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009988687","display_name":"Francesco P. Battaglia","orcid":"https://orcid.org/0000-0003-3715-8875"},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]},{"id":"https://openalex.org/I4210108594","display_name":"Amsterdam Neuroscience","ror":"https://ror.org/01x2d9f70","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210108594"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Francesco P. Battaglia","raw_affiliation_strings":["Center for Neuroscience, University of Amsterdam, Amsterdam, Netherlands","Center for Neuroscience, University of Amsterdam, Amsterdam, The Netherlands, 1098 XH"],"affiliations":[{"raw_affiliation_string":"Center for Neuroscience, University of Amsterdam, Amsterdam, Netherlands","institution_ids":["https://openalex.org/I4210108594","https://openalex.org/I887064364"]},{"raw_affiliation_string":"Center for Neuroscience, University of Amsterdam, Amsterdam, The Netherlands, 1098 XH","institution_ids":["https://openalex.org/I887064364"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018991038","display_name":"V.B. Balakirsky","orcid":null},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Vladimir B. Balakirsky","raw_affiliation_strings":["Institute for Experimental Mathematics, University of Essen, Essen, Germany","Institute for Experimental Mathematics, University of Essen, Essen, Germany, 45326"],"affiliations":[{"raw_affiliation_string":"Institute for Experimental Mathematics, University of Essen, Essen, Germany","institution_ids":["https://openalex.org/I62318514"]},{"raw_affiliation_string":"Institute for Experimental Mathematics, University of Essen, Essen, Germany, 45326","institution_ids":["https://openalex.org/I62318514"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065607012","display_name":"A. J. Han Vinck","orcid":"https://orcid.org/0000-0002-7756-5304"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"A. J. Han Vinck","raw_affiliation_strings":["Institute for Experimental Mathematics, University of Essen, Essen, Germany","Institute for Experimental Mathematics, University of Essen, Essen, Germany, 45326"],"affiliations":[{"raw_affiliation_string":"Institute for Experimental Mathematics, University of Essen, Essen, Germany","institution_ids":["https://openalex.org/I62318514"]},{"raw_affiliation_string":"Institute for Experimental Mathematics, University of Essen, Essen, Germany, 45326","institution_ids":["https://openalex.org/I62318514"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051130900","display_name":"Cyriel M. A. Pennartz","orcid":"https://orcid.org/0000-0001-8328-1175"},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]},{"id":"https://openalex.org/I4210108594","display_name":"Amsterdam Neuroscience","ror":"https://ror.org/01x2d9f70","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210108594"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Cyriel Pennartz","raw_affiliation_strings":["Center for Neuroscience, University of Amsterdam, Amsterdam, Netherlands","Center for Neuroscience, University of Amsterdam, Amsterdam, The Netherlands, 1098 XH"],"affiliations":[{"raw_affiliation_string":"Center for Neuroscience, University of Amsterdam, Amsterdam, Netherlands","institution_ids":["https://openalex.org/I4210108594","https://openalex.org/I887064364"]},{"raw_affiliation_string":"Center for Neuroscience, University of Amsterdam, Amsterdam, The Netherlands, 1098 XH","institution_ids":["https://openalex.org/I887064364"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5033216984"],"corresponding_institution_ids":["https://openalex.org/I4210108594","https://openalex.org/I887064364"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07383595,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"1054","last_page":"1058"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9850999712944031,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9850999712944031,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9814000129699707,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9771999716758728,"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/remainder","display_name":"Remainder","score":0.7832326292991638},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7554372549057007},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5839704275131226},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5540623664855957},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5172775387763977},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.44824063777923584},{"id":"https://openalex.org/keywords/cross-entropy","display_name":"Cross entropy","score":0.4450428783893585},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4431857168674469},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.4265921711921692},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.42374303936958313},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35681450366973877},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33794844150543213},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23649901151657104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12268170714378357}],"concepts":[{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.7832326292991638},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7554372549057007},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5839704275131226},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5540623664855957},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5172775387763977},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.44824063777923584},{"id":"https://openalex.org/C167981619","wikidata":"https://www.wikidata.org/wiki/Q1685498","display_name":"Cross entropy","level":3,"score":0.4450428783893585},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4431857168674469},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4265921711921692},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.42374303936958313},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35681450366973877},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33794844150543213},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23649901151657104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12268170714378357},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2012.6283012","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6283012","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-article"},{"id":"pmh:uvapub:oai:dare.uva.nl:publications/ca1fd36f-c0a5-47e8-a83f-3569b2672040","is_oa":false,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/estimation-of-the-entropy-on-the-basis-of-its-polynomial-representation(ca1fd36f-c0a5-47e8-a83f-3569b2672040).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2012 IEEE International Symposium on Information Theory proceedings (ISIT 2012): Cambridge, Massachusetts, USA, 1-6 July 2012, 1054 - 1058","raw_type":"info:eu-repo/semantics/conferencepaper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1992536060","https://openalex.org/W1995875735","https://openalex.org/W2091134111","https://openalex.org/W2097173970","https://openalex.org/W2097636360","https://openalex.org/W2114771311"],"related_works":["https://openalex.org/W4315487898","https://openalex.org/W2088904828","https://openalex.org/W617989196","https://openalex.org/W2032199336","https://openalex.org/W2904183727","https://openalex.org/W2347282152","https://openalex.org/W2140321063","https://openalex.org/W2039575089","https://openalex.org/W4385351587","https://openalex.org/W4372064123"],"abstract_inverted_index":{"An":[0],"algorithm":[1],"for":[2],"estimating":[3],"the":[4,10,13,17,24,29,41,44,50,56,63,66,72,79],"entropy,":[5],"which":[6],"is":[7,31],"based":[8],"on":[9],"representation":[11],"of":[12,19,40,43,65],"entropy":[14],"function":[15,27,47],"as":[16,69],"sum":[18],"two":[20],"polynomial":[21,25,45],"terms,":[22],"called":[23],"approximation":[26,46],"and":[28,37,48],"remainder,":[30],"proposed.":[32],"We":[33],"construct":[34],"an":[35],"accurate":[36],"unbiased":[38],"estimate":[39,55,68],"value":[42],"use":[49],"known":[51,73],"Bayesian":[52],"approach":[53],"to":[54,71],"remainder.":[57],"The":[58],"combined":[59],"estimator":[60],"essentially":[61],"reduces":[62],"bias":[64],"constructed":[67],"compared":[70],"estimators.":[74],"Simulation":[75],"results":[76],"that":[77],"confirm":[78],"claim":[80],"are":[81],"presented.":[82]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}