{"id":"https://openalex.org/W2081988641","doi":"https://doi.org/10.3390/e16042161","title":"Quantifying Unique Information","display_name":"Quantifying Unique Information","publication_year":2014,"publication_date":"2014-04-15","ids":{"openalex":"https://openalex.org/W2081988641","doi":"https://doi.org/10.3390/e16042161","mag":"2081988641"},"language":"en","primary_location":{"id":"doi:10.3390/e16042161","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16042161","pdf_url":"https://www.mdpi.com/1099-4300/16/4/2161/pdf?version=1424785392","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":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/16/4/2161/pdf?version=1424785392","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017316523","display_name":"Nils Bertschinger","orcid":"https://orcid.org/0000-0002-6699-9596"},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Nils Bertschinger","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, Inselstra\u00dfe 23, 04109 Leipzig, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, Inselstra\u00dfe 23, 04109 Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053941878","display_name":"Johannes Rauh","orcid":"https://orcid.org/0000-0001-6411-7775"},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Johannes Rauh","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, Inselstra\u00dfe 23, 04109 Leipzig, Germany"],"raw_orcid":"https://orcid.org/0000-0001-6411-7775","affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, Inselstra\u00dfe 23, 04109 Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074755166","display_name":"Eckehard Olbrich","orcid":"https://orcid.org/0000-0002-3987-1271"},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Eckehard Olbrich","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, Inselstra\u00dfe 23, 04109 Leipzig, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, Inselstra\u00dfe 23, 04109 Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072990982","display_name":"J\u00fcrgen Jost","orcid":"https://orcid.org/0000-0001-5258-6590"},"institutions":[{"id":"https://openalex.org/I1308548392","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35","country_code":"US","type":"funder","lineage":["https://openalex.org/I1308548392"]},{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"J\u00fcrgen Jost","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, Inselstra\u00dfe 23, 04109 Leipzig, Germany","Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, Inselstra\u00dfe 23, 04109 Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327"]},{"raw_affiliation_string":"Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA","institution_ids":["https://openalex.org/I1308548392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065926474","display_name":"Nihat Ay","orcid":"https://orcid.org/0000-0002-8527-2579"},"institutions":[{"id":"https://openalex.org/I1308548392","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35","country_code":"US","type":"funder","lineage":["https://openalex.org/I1308548392"]},{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Nihat Ay","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, Inselstra\u00dfe 23, 04109 Leipzig, Germany","Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, Inselstra\u00dfe 23, 04109 Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327"]},{"raw_affiliation_string":"Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA","institution_ids":["https://openalex.org/I1308548392"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053941878"],"corresponding_institution_ids":["https://openalex.org/I4210091327"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":22.2291,"has_fulltext":false,"cited_by_count":290,"citation_normalized_percentile":{"value":0.99510066,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"16","issue":"4","first_page":"2161","last_page":"2183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11031","display_name":"Game Theory and Applications","score":0.9804999828338623,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"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/T11716","display_name":"Random Matrices and Applications","score":0.9559999704360962,"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/mutual-information","display_name":"Mutual information","score":0.7060295343399048},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6939359903335571},{"id":"https://openalex.org/keywords/interaction-information","display_name":"Interaction information","score":0.6165348291397095},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.5825360417366028},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5511575937271118},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5350950956344604},{"id":"https://openalex.org/keywords/conditional-mutual-information","display_name":"Conditional mutual information","score":0.45099425315856934},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43975698947906494},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3767912983894348},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.21455508470535278}],"concepts":[{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.7060295343399048},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6939359903335571},{"id":"https://openalex.org/C38764148","wikidata":"https://www.wikidata.org/wiki/Q17098245","display_name":"Interaction information","level":2,"score":0.6165348291397095},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.5825360417366028},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5511575937271118},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5350950956344604},{"id":"https://openalex.org/C124805900","wikidata":"https://www.wikidata.org/wiki/Q5159269","display_name":"Conditional mutual information","level":3,"score":0.45099425315856934},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43975698947906494},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3767912983894348},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21455508470535278},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.3390/e16042161","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16042161","pdf_url":"https://www.mdpi.com/1099-4300/16/4/2161/pdf?version=1424785392","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":"pmh:oai:arXiv.org:1311.2852","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.2852","pdf_url":"https://arxiv.org/pdf/1311.2852","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.706.2283","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.706.2283","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mis.mpg.de/preprints/2013/preprint2013_102.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.766.342","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.766.342","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1311.2852.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:e95b48f2bba242cdb4f6d4c328df0ab0","is_oa":true,"landing_page_url":"https://doaj.org/article/e95b48f2bba242cdb4f6d4c328df0ab0","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 16, Iss 4, Pp 2161-2183 (2014)","raw_type":"article"},{"id":"pmh:oai:edoc.mpg.de:708573","is_oa":false,"landing_page_url":"http://edoc.mpg.de/708573","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, v.16, 2161-2183 (2014)","raw_type":"Article"},{"id":"pmh:oai:mdpi.com:/1099-4300/16/4/2161/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e16042161","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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; Volume 16; Issue 4; Pages: 2161-2183","raw_type":"Text"},{"id":"pmh:oai:tore.tuhh.de:11420/14055","is_oa":false,"landing_page_url":"http://hdl.handle.net/11420/14055","pdf_url":null,"source":{"id":"https://openalex.org/S4306401751","display_name":"tub.dok (Hamburg University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I884043246","host_organization_name":"Hamburg University of Technology","host_organization_lineage":["https://openalex.org/I884043246"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.3390/e16042161","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16042161","pdf_url":"https://www.mdpi.com/1099-4300/16/4/2161/pdf?version=1424785392","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":[{"id":"https://metadata.un.org/sdg/10","score":0.6000000238418579,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2081988641.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1866114900","https://openalex.org/W1932088538","https://openalex.org/W1933178270","https://openalex.org/W1965370802","https://openalex.org/W1990576250","https://openalex.org/W2024616265","https://openalex.org/W2037667080","https://openalex.org/W2050495532","https://openalex.org/W2116811583","https://openalex.org/W2139708568","https://openalex.org/W2152587044","https://openalex.org/W2887002214","https://openalex.org/W3099025165","https://openalex.org/W3101379241","https://openalex.org/W4300972832"],"related_works":["https://openalex.org/W4205619203","https://openalex.org/W4390964098","https://openalex.org/W4296367141","https://openalex.org/W3135541457","https://openalex.org/W3212925274","https://openalex.org/W2044289181","https://openalex.org/W4313429060","https://openalex.org/W2057609120","https://openalex.org/W4225940264","https://openalex.org/W2111510771"],"abstract_inverted_index":{"We":[0,117],"propose":[1],"new":[2,95],"measures":[3,36,83,111,122],"of":[4,21,24,43,61,84,120],"shared":[5,49,85],"information,":[6,45],"unique":[7,44,52],"information":[8,11,20,50,53],"and":[9,51,66,123],"synergistic":[10],"that":[12,48,100,103],"can":[13],"be":[14],"used":[15],"to":[16,108,126],"decompose":[17],"the":[18,58,62,101,113],"mutual":[19],"a":[22,30],"pair":[23],"random":[25,32],"variables":[26],"(Y,":[27],"Z)":[28],"with":[29],"third":[31],"variable":[33],"X.":[34],"Our":[35],"are":[37,106],"motivated":[38],"by":[39,80],"an":[40],"operational":[41],"idea":[42],"which":[46],"suggests":[47],"should":[54],"depend":[55],"only":[56],"on":[57],"marginal":[59],"distributions":[60],"pairs":[63],"(X,":[64],"Y)":[65],"(X,Z).":[67],"Although":[68],"this":[69],"invariance":[70,88,115],"property":[71,89],"has":[72],"not":[73,91],"been":[74],"studied":[75],"before,":[76],"it":[77,98],"is":[78],"satisfied":[79],"other":[81,110,127],"proposed":[82],"information.":[86],"The":[87],"does":[90],"uniquely":[92],"determine":[93],"our":[94,121],"measures,":[96],"but":[97],"implies":[99],"functions":[102],"we":[104],"define":[105],"bounds":[107],"any":[109],"satisfying":[112],"same":[114],"property.":[116],"study":[118],"properties":[119],"compare":[124],"them":[125],"candidate":[128],"measures.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":18},{"year":2025,"cited_by_count":27},{"year":2024,"cited_by_count":26},{"year":2023,"cited_by_count":25},{"year":2022,"cited_by_count":21},{"year":2021,"cited_by_count":22},{"year":2020,"cited_by_count":34},{"year":2019,"cited_by_count":26},{"year":2018,"cited_by_count":30},{"year":2017,"cited_by_count":30},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":6}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
