{"id":"https://openalex.org/W7143398832","doi":"https://doi.org/10.3390/e28040381","title":"Numerical Evaluation of Gaussian Mixture Entropy","display_name":"Numerical Evaluation of Gaussian Mixture Entropy","publication_year":2026,"publication_date":"2026-03-30","ids":{"openalex":"https://openalex.org/W7143398832","doi":"https://doi.org/10.3390/e28040381","pmid":"https://pubmed.ncbi.nlm.nih.gov/42072506"},"language":"en","primary_location":{"id":"doi:10.3390/e28040381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28040381","pdf_url":"https://www.mdpi.com/1099-4300/28/4/381/pdf?version=1774862172","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/28/4/381/pdf?version=1774862172","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025719450","display_name":"Basheer Joudeh","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Basheer Joudeh","raw_affiliation_strings":["Department of Computer Science and Mathematics, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-8311-6161","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Mathematics, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5125241027","display_name":"Boris \u0160kori\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Boris \u0160kori\u0107","raw_affiliation_strings":["Department of Computer Science and Mathematics, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0003-1409-4127","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Mathematics, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025719450","https://openalex.org/A5125241027"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.56096248,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"4","first_page":"381","last_page":"381"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.46209999918937683,"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"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.46209999918937683,"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"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.10949999839067459,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.05339999869465828,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5928000211715698},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.573199987411499},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.5339999794960022},{"id":"https://openalex.org/keywords/differential-entropy","display_name":"Differential entropy","score":0.48339998722076416},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4830999970436096},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"Numerical approximation","score":0.375900000333786},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.3758000135421753},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.3433000147342682}],"concepts":[{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5928000211715698},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.573199987411499},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5728999972343445},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.5339999794960022},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4876999855041504},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.48399999737739563},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.48339998722076416},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4830999970436096},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.375900000333786},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.3758000135421753},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3433000147342682},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.3140000104904175},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.30410000681877136},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.30070000886917114},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.28349998593330383},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.2800000011920929},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.2615000009536743}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e28040381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28040381","pdf_url":"https://www.mdpi.com/1099-4300/28/4/381/pdf?version=1774862172","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:42072506","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42072506","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,"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":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pure.tue.nl:openaire/580a6848-1dc4-4794-8be0-b8273ee6ad30","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/580a6848-1dc4-4794-8be0-b8273ee6ad30","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Joudeh, B & \u0160kori\u0107, B 2026, 'Numerical Evaluation of Gaussian Mixture Entropy', Entropy, vol. 28, no. 4, 381. https://doi.org/10.3390/e28040381","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pubmedcentral.nih.gov:13114422","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13114422/","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13114422/pdf/entropy-28-00381.pdf","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:cc1354f295754ccf9d4f2b4b080010ed","is_oa":true,"landing_page_url":"https://doaj.org/article/cc1354f295754ccf9d4f2b4b080010ed","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 28, Iss 4, p 381 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e28040381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28040381","pdf_url":"https://www.mdpi.com/1099-4300/28/4/381/pdf?version=1774862172","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4390631491","display_name":null,"funder_award_id":"CS.001","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7143398832.pdf","grobid_xml":"https://content.openalex.org/works/W7143398832.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1973057461","https://openalex.org/W1992140187","https://openalex.org/W2006245542","https://openalex.org/W2014870251","https://openalex.org/W2033178790","https://openalex.org/W2059659103","https://openalex.org/W2076980137","https://openalex.org/W2082612735","https://openalex.org/W2141652941","https://openalex.org/W2145590522","https://openalex.org/W2168980979","https://openalex.org/W2574669229","https://openalex.org/W2766502430","https://openalex.org/W2795528501","https://openalex.org/W2804750906","https://openalex.org/W2890823802","https://openalex.org/W2891047800","https://openalex.org/W3018531073","https://openalex.org/W3148595793","https://openalex.org/W4233798822","https://openalex.org/W4389664923","https://openalex.org/W4396667906","https://openalex.org/W4404509772","https://openalex.org/W4407564361"],"related_works":[],"abstract_inverted_index":{"-component":[0],"Gaussian":[1],"mixture":[2],"in":[3,58],"Rn.":[4],"We":[5,19],"provide":[6],"two":[7],"examples":[8],"of":[9],"approximations":[10,57],"using":[11],"our":[12],"method":[13],"denoted":[14],"by":[15],"h\u00afC,mTaylor(X)":[16,22],"and":[17,35,47],"h\u00afCPolyfit(X).":[18],"show":[20],"that":[21],"provides":[23,32],"an":[24,33],"easy-to-compute":[25],"lower":[26],"bound":[27],"to":[28,38,50],"h(X),":[29],"while":[30],"h\u00afCPolyfit(X)":[31,40],"accurate":[34,43],"efficient":[36],"approximation":[37],"h(X).":[39],"is":[41,48],"more":[42,53],"than":[44,55],"known":[45],"bounds":[46],"conjectured":[49],"be":[51],"much":[52],"resilient":[54],"other":[56],"high":[59],"dimensions.":[60]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-03-31T00:00:00"}
