{"id":"https://openalex.org/W2146567666","doi":"https://doi.org/10.1162/089976698300017205","title":"Probability Density Estimation Using Entropy Maximization","display_name":"Probability Density Estimation Using Entropy Maximization","publication_year":1998,"publication_date":"1998-10-01","ids":{"openalex":"https://openalex.org/W2146567666","doi":"https://doi.org/10.1162/089976698300017205","mag":"2146567666","pmid":"https://pubmed.ncbi.nlm.nih.gov/9744904"},"language":"en","primary_location":{"id":"doi:10.1162/089976698300017205","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976698300017205","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5028328218","display_name":"Gad Miller","orcid":"https://orcid.org/0000-0002-7196-6529"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Gad Miller","raw_affiliation_strings":["School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel","School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 69978, Israel"],"affiliations":[{"raw_affiliation_string":"School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 69978, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001249894","display_name":"D. Horn","orcid":"https://orcid.org/0000-0003-2708-186X"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"David Horn","raw_affiliation_strings":["School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel","School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 69978, Israel"],"affiliations":[{"raw_affiliation_string":"School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 69978, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028328218"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":2.197,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.90021606,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"10","issue":"7","first_page":"1925","last_page":"1938"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9997000098228455,"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/T10320","display_name":"Neural Networks and Applications","score":0.9997000098228455,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9886000156402588,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy-maximization","display_name":"Entropy maximization","score":0.8227100372314453},{"id":"https://openalex.org/keywords/expectation\u2013maximization-algorithm","display_name":"Expectation\u2013maximization algorithm","score":0.6439155340194702},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.6018321514129639},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5554806590080261},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5305920839309692},{"id":"https://openalex.org/keywords/density-estimation","display_name":"Density estimation","score":0.5116382241249084},{"id":"https://openalex.org/keywords/conditional-probability-distribution","display_name":"Conditional probability distribution","score":0.5107429027557373},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5097314715385437},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.494895875453949},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.48905786871910095},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4761669337749481},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.46614328026771545},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"Conditional entropy","score":0.45752227306365967},{"id":"https://openalex.org/keywords/cross-entropy","display_name":"Cross entropy","score":0.4186505079269409},{"id":"https://openalex.org/keywords/marginal-distribution","display_name":"Marginal distribution","score":0.4138118624687195},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.380143940448761},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3719494342803955},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.1947082281112671},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.1825578212738037},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1815301775932312},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.0957883894443512}],"concepts":[{"id":"https://openalex.org/C127233936","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Entropy maximization","level":3,"score":0.8227100372314453},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.6439155340194702},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.6018321514129639},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5554806590080261},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5305920839309692},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.5116382241249084},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.5107429027557373},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5097314715385437},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.494895875453949},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.48905786871910095},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4761669337749481},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.46614328026771545},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.45752227306365967},{"id":"https://openalex.org/C167981619","wikidata":"https://www.wikidata.org/wiki/Q1685498","display_name":"Cross entropy","level":3,"score":0.4186505079269409},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.4138118624687195},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.380143940448761},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3719494342803955},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.1947082281112671},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.1825578212738037},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1815301775932312},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0957883894443512},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1162/089976698300017205","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976698300017205","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:9744904","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/9744904","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":"Neural computation","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.49.5860","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.5860","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.brain.tau.ac.il/~horn/./publications/ME.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1554663460","https://openalex.org/W1589277047","https://openalex.org/W2026799324","https://openalex.org/W2042492924","https://openalex.org/W2082195896","https://openalex.org/W2099111195","https://openalex.org/W2108384452","https://openalex.org/W2121807556","https://openalex.org/W2143132653","https://openalex.org/W2341283081","https://openalex.org/W3022628558","https://openalex.org/W4231370560","https://openalex.org/W4255825300"],"related_works":["https://openalex.org/W4205235378","https://openalex.org/W1657743638","https://openalex.org/W1925823181","https://openalex.org/W2950354394","https://openalex.org/W2040672625","https://openalex.org/W2139507220","https://openalex.org/W4287330836","https://openalex.org/W2625653665","https://openalex.org/W4245952386","https://openalex.org/W2065107791"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,35,70],"method":[3],"for":[4],"estimating":[5],"probability":[6,63],"density":[7,11],"functions":[8,12],"and":[9],"conditional":[10],"by":[13,18,87],"training":[14],"on":[15],"data":[16,77],"produced":[17],"such":[19],"distributions.":[20],"The":[21,52,65,82],"algorithm":[22,57,83],"employs":[23],"new":[24],"stochastic":[25,91],"variables":[26],"that":[27],"amount":[28],"to":[29,43,47,94],"coding":[30],"of":[31,37,55,61,76],"the":[32,48,56,62,79],"input,":[33],"using":[34,90],"principle":[36],"entropy":[38,96],"maximization.":[39,97],"It":[40],"is":[41,84],"shown":[42],"be":[44],"closely":[45],"related":[46],"maximum":[49],"likelihood":[50],"approach.":[51],"encoding":[53],"step":[54,67],"provides":[58],"an":[59,74],"estimate":[60],"distribution.":[64,81],"decoding":[66],"serves":[68],"as":[69],"generative":[71],"mode,":[72],"producing":[73],"ensemble":[75],"with":[78],"desired":[80],"readily":[85],"implemented":[86],"neural":[88],"networks,":[89],"gradient":[92],"ascent":[93],"achieve":[95]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}