{"id":"https://openalex.org/W2024993643","doi":"https://doi.org/10.3390/e15030721","title":"Minimum Mutual Information and Non-Gaussianity through the Maximum Entropy Method: Estimation from Finite Samples","display_name":"Minimum Mutual Information and Non-Gaussianity through the Maximum Entropy Method: Estimation from Finite Samples","publication_year":2013,"publication_date":"2013-02-25","ids":{"openalex":"https://openalex.org/W2024993643","doi":"https://doi.org/10.3390/e15030721","mag":"2024993643"},"language":"en","primary_location":{"id":"doi:10.3390/e15030721","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e15030721","pdf_url":"https://www.mdpi.com/1099-4300/15/3/721/pdf?version=1424785000","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/15/3/721/pdf?version=1424785000","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016348981","display_name":"Carlos Pires","orcid":"https://orcid.org/0000-0002-1700-6607"},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Carlos Pires","raw_affiliation_strings":["Instituto Dom Luiz (IDL), University of Lisbon (UL), Lisbon, P-1749-016, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto Dom Luiz (IDL), University of Lisbon (UL), Lisbon, P-1749-016, Portugal","institution_ids":["https://openalex.org/I141596103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063536272","display_name":"Rui A. P. Perdig\u00e3o","orcid":"https://orcid.org/0000-0001-5543-1754"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Rui Perdig\u00e3o","raw_affiliation_strings":["Institute of Hydraulic Engineering and Water Resources Management, Vienna University of Technology, Vienna, A-1040, Austria"],"raw_orcid":"https://orcid.org/0000-0001-5543-1754","affiliations":[{"raw_affiliation_string":"Institute of Hydraulic Engineering and Water Resources Management, Vienna University of Technology, Vienna, A-1040, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.6008,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.82884065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"3","first_page":"721","last_page":"752"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9994999766349792,"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":0.9994999766349792,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.983299970626831,"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/mathematics","display_name":"Mathematics","score":0.8383932709693909},{"id":"https://openalex.org/keywords/quantile","display_name":"Quantile","score":0.5878132581710815},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.5783156156539917},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5290265083312988},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4965875744819641},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.48749566078186035},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47210612893104553},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.46991434693336487},{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"Joint probability distribution","score":0.4558098018169403},{"id":"https://openalex.org/keywords/joint-entropy","display_name":"Joint entropy","score":0.41670602560043335},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.3919283449649811},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35177478194236755}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8383932709693909},{"id":"https://openalex.org/C118671147","wikidata":"https://www.wikidata.org/wiki/Q578714","display_name":"Quantile","level":2,"score":0.5878132581710815},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.5783156156539917},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5290265083312988},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4965875744819641},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.48749566078186035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47210612893104553},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.46991434693336487},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.4558098018169403},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.41670602560043335},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.3919283449649811},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35177478194236755},{"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":2,"locations":[{"id":"doi:10.3390/e15030721","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e15030721","pdf_url":"https://www.mdpi.com/1099-4300/15/3/721/pdf?version=1424785000","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:75913b0d7d9249e0890f5f3826212eab","is_oa":true,"landing_page_url":"https://doaj.org/article/75913b0d7d9249e0890f5f3826212eab","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 15, Iss 3, Pp 721-752 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e15030721","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e15030721","pdf_url":"https://www.mdpi.com/1099-4300/15/3/721/pdf?version=1424785000","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7599999904632568,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2024993643.pdf","grobid_xml":"https://content.openalex.org/works/W2024993643.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W404240460","https://openalex.org/W613625395","https://openalex.org/W1460189015","https://openalex.org/W1586973386","https://openalex.org/W1594224465","https://openalex.org/W1599132067","https://openalex.org/W1623248653","https://openalex.org/W1661915592","https://openalex.org/W1947089506","https://openalex.org/W1972764827","https://openalex.org/W1973475129","https://openalex.org/W1995875735","https://openalex.org/W1998050452","https://openalex.org/W1999308953","https://openalex.org/W2018490621","https://openalex.org/W2034357970","https://openalex.org/W2037208163","https://openalex.org/W2041404167","https://openalex.org/W2049420890","https://openalex.org/W2052958516","https://openalex.org/W2061119788","https://openalex.org/W2073982870","https://openalex.org/W2090804142","https://openalex.org/W2091134111","https://openalex.org/W2092435780","https://openalex.org/W2099111195","https://openalex.org/W2109584604","https://openalex.org/W2113051562","https://openalex.org/W2113848012","https://openalex.org/W2114771311","https://openalex.org/W2119436275","https://openalex.org/W2121943534","https://openalex.org/W2146697888","https://openalex.org/W2151376060","https://openalex.org/W2161401775","https://openalex.org/W2164708354","https://openalex.org/W2169135475","https://openalex.org/W2531457713","https://openalex.org/W2795383965","https://openalex.org/W2964235834","https://openalex.org/W2964243709","https://openalex.org/W3103962224","https://openalex.org/W3105788277","https://openalex.org/W3122572058","https://openalex.org/W4241861175","https://openalex.org/W4250391581","https://openalex.org/W4285719527","https://openalex.org/W6613934775","https://openalex.org/W6634905366","https://openalex.org/W6637601281","https://openalex.org/W6681422526","https://openalex.org/W6728927983"],"related_works":["https://openalex.org/W1479897377","https://openalex.org/W3134129340","https://openalex.org/W2036846997","https://openalex.org/W2533038408","https://openalex.org/W2158886050","https://openalex.org/W2509725027","https://openalex.org/W2133435412","https://openalex.org/W4300707824","https://openalex.org/W2950438842","https://openalex.org/W2167163570"],"abstract_inverted_index":{"The":[0],"Minimum":[1],"Mutual":[2],"Information":[3],"(MinMI)":[4],"Principle":[5],"provides":[6],"the":[7,63,73,80,99,105,123,137,203],"least":[8],"committed,":[9],"maximum-joint-entropy":[10],"(ME)":[11],"inferential":[12],"law":[13],"that":[14,192],"is":[15,122,213],"compatible":[16],"with":[17],"prescribed":[18],"marginal":[19],"distributions":[20],"and":[21,86,174,211],"empirical":[22],"cross":[23,76],"constraints.":[24],"Here,":[25],"we":[26,165],"estimate":[27],"MI":[28,180],"bounds":[29],"(the":[30],"MinMI":[31,81,106,206],"values)":[32],"generated":[33],"by":[34,39,59],"constraining":[35],"sets":[36,112],"Tcr":[37,90],"comprehended":[38],"mcr":[40],"linear":[41],"and/or":[42],"nonlinear":[43],"joint":[44,189],"expectations,":[45],"computed":[46],"from":[47],"samples":[48],"of":[49,62,75,118,179],"N":[50,129,133],"iid":[51],"outcomes.":[52],"Marginals":[53],"(and":[54],"their":[55],"entropy)":[56],"are":[57,69],"imposed":[58],"single":[60],"morphisms":[61],"original":[64],"random":[65],"variables.":[66],"N-asymptotic":[67],"formulas":[68],"given":[70],"both":[71],"for":[72,217],"distribution":[74,147],"expectation\u2019s":[77],"estimation":[78,82],"errors,":[79],"bias,":[83,207],"its":[84],"variance":[85],"distribution.":[87],"A":[88],"growing":[89],"leads":[91],"to":[92,98,109,169,183,188],"an":[93,163],"increasing":[94],"MinMI,":[95],"converging":[96],"eventually":[97],"total":[100],"MI.":[101,161],"Under":[102],"N-sized":[103],"samples,":[104],"increment":[107],"relative":[108],"two":[110,138],"encapsulated":[111],"Tcr1":[113],"\u2282":[114],"Tcr2":[115],"(with":[116],"numbers":[117],"constraints":[119,155],"mcr1&lt;mcr2":[120],")":[121],"test-difference":[124],"\u03b4H":[125,143],"=":[126],"Hmax":[127,131],"1,":[128],"-":[130],"2,":[132],"\u2265":[134],"0":[135],"between":[136,205],"respective":[139],"estimated":[140],"MEs.":[141],"Asymptotically,":[142],"follows":[144],"a":[145,177],"Chi-Squared":[146],"1/2N\u03a72":[148],"(mcr2-mcr1)":[149],"whose":[150],"upper":[151],"quantiles":[152],"determine":[153],"if":[154],"in":[156,193,215],"Tcr2/Tcr1":[157],"explain":[158],"significant":[159],"extra":[160],"As":[162],"example,":[164],"have":[166,175],"set":[167],"marginals":[168],"being":[170],"normally":[171],"distributed":[172],"(Gaussian)":[173],"built":[176],"sequence":[178],"bounds,":[181],"associated":[182],"successive":[184],"non-linear":[185],"correlations":[186],"due":[187],"non-Gaussianity.":[190],"Noting":[191],"real-world":[194],"situations":[195],"available":[196],"sample":[197],"sizes":[198],"can":[199],"be":[200],"rather":[201],"low,":[202],"relationship":[204],"probability":[208],"density":[209],"over-fitting":[210],"outliers":[212],"put":[214],"evidence":[216],"under-sampled":[218],"data.":[219]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
