{"id":"https://openalex.org/W2997176264","doi":"https://doi.org/10.14736/kyb-2021-3-0383","title":"Properties of unique information","display_name":"Properties of unique information","publication_year":2021,"publication_date":"2021-07-07","ids":{"openalex":"https://openalex.org/W2997176264","doi":"https://doi.org/10.14736/kyb-2021-3-0383","mag":"2997176264"},"language":"en","primary_location":{"id":"doi:10.14736/kyb-2021-3-0383","is_oa":true,"landing_page_url":"https://doi.org/10.14736/kyb-2021-3-0383","pdf_url":"https://www.kybernetika.cz/content/2021/3/383/paper.pdf","source":{"id":"https://openalex.org/S158577884","display_name":"Kybernetika","issn_l":"0023-5954","issn":["0023-5954","1805-949X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310314340","host_organization_name":"Institute of Information Theory and Automation of the Czech Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310314340","https://openalex.org/P4310314171"],"host_organization_lineage_names":["Institute of Information Theory and Automation of the Czech Academy of Sciences","Czech Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kybernetika","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.kybernetika.cz/content/2021/3/383/paper.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053941878","display_name":"Johannes Rauh","orcid":"https://orcid.org/0000-0001-6411-7775"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Johannes Rauh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011900642","display_name":"Maik Sch\u00fcnemann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maik Sch\u00fcnemann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5072990982","display_name":"J\u00fcrgen Jost","orcid":"https://orcid.org/0000-0001-5258-6590"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J\u00fcrgen Jost","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2903,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65047968,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"383","last_page":"403"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.986299991607666,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.986299991607666,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9821000099182129,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9786999821662903,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/uniqueness","display_name":"Uniqueness","score":0.8687267303466797},{"id":"https://openalex.org/keywords/conditional-independence","display_name":"Conditional independence","score":0.799156665802002},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.6299618482589722},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5934348702430725},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5896593332290649},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5733485817909241},{"id":"https://openalex.org/keywords/conditional-probability","display_name":"Conditional probability","score":0.5215097069740295},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5063387155532837},{"id":"https://openalex.org/keywords/conditional-probability-distribution","display_name":"Conditional probability distribution","score":0.4671781659126282},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4625064730644226},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4559723138809204},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.44319090247154236},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44192466139793396},{"id":"https://openalex.org/keywords/conditional-dependence","display_name":"Conditional dependence","score":0.41565749049186707},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3570649027824402},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3400251269340515},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33423131704330444},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2567269802093506},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14897119998931885},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.14635047316551208},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09248360991477966}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8687267303466797},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.799156665802002},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.6299618482589722},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5934348702430725},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5896593332290649},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5733485817909241},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.5215097069740295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5063387155532837},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.4671781659126282},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4625064730644226},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4559723138809204},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.44319090247154236},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44192466139793396},{"id":"https://openalex.org/C174920663","wikidata":"https://www.wikidata.org/wiki/Q5159256","display_name":"Conditional dependence","level":2,"score":0.41565749049186707},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3570649027824402},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3400251269340515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33423131704330444},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2567269802093506},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14897119998931885},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.14635047316551208},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09248360991477966},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.14736/kyb-2021-3-0383","is_oa":true,"landing_page_url":"https://doi.org/10.14736/kyb-2021-3-0383","pdf_url":"https://www.kybernetika.cz/content/2021/3/383/paper.pdf","source":{"id":"https://openalex.org/S158577884","display_name":"Kybernetika","issn_l":"0023-5954","issn":["0023-5954","1805-949X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310314340","host_organization_name":"Institute of Information Theory and Automation of the Czech Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310314340","https://openalex.org/P4310314171"],"host_organization_lineage_names":["Institute of Information Theory and Automation of the Czech Academy of Sciences","Czech Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kybernetika","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1912.12505","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.12505","pdf_url":"https://arxiv.org/pdf/1912.12505","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:oai.dml.cz:10338.dmlcz/149197","is_oa":true,"landing_page_url":"http://hdl.handle.net/10338.dmlcz/149197","pdf_url":"http://dml.cz/bitstream/handle/10338.dmlcz/149197/Kybernetika_57-2021-3_1.pdf","source":{"id":"https://openalex.org/S4406922294","display_name":"Czech digital mathematics library","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":null,"raw_type":"type:math"},{"id":"mag:2997176264","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1912.12505.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1912.12505","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1912.12505","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.14736/kyb-2021-3-0383","is_oa":true,"landing_page_url":"https://doi.org/10.14736/kyb-2021-3-0383","pdf_url":"https://www.kybernetika.cz/content/2021/3/383/paper.pdf","source":{"id":"https://openalex.org/S158577884","display_name":"Kybernetika","issn_l":"0023-5954","issn":["0023-5954","1805-949X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310314340","host_organization_name":"Institute of Information Theory and Automation of the Czech Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310314340","https://openalex.org/P4310314171"],"host_organization_lineage_names":["Institute of Information Theory and Automation of the Czech Academy of Sciences","Czech Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kybernetika","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4300000071525574,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2997176264.pdf","grobid_xml":"https://content.openalex.org/works/W2997176264.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1932088538","https://openalex.org/W1973128036","https://openalex.org/W2016935849","https://openalex.org/W2037667080","https://openalex.org/W2051494150","https://openalex.org/W2081988641","https://openalex.org/W2760912253","https://openalex.org/W2896560559","https://openalex.org/W2963492916","https://openalex.org/W2975994619","https://openalex.org/W3100917360","https://openalex.org/W3100944861","https://openalex.org/W3101379241","https://openalex.org/W3103979701","https://openalex.org/W3104924683","https://openalex.org/W3106459576","https://openalex.org/W4229633200"],"related_works":["https://openalex.org/W3177678412","https://openalex.org/W2050984837","https://openalex.org/W1633412631","https://openalex.org/W2334419599","https://openalex.org/W1968976114","https://openalex.org/W2770203142","https://openalex.org/W2587848051","https://openalex.org/W3029871589","https://openalex.org/W3101686413","https://openalex.org/W2963125162","https://openalex.org/W2017367830","https://openalex.org/W2289014066","https://openalex.org/W2952638844","https://openalex.org/W2405064337","https://openalex.org/W1484071118","https://openalex.org/W2952166317","https://openalex.org/W2065056154","https://openalex.org/W2187118397","https://openalex.org/W2007008704","https://openalex.org/W1259894574"],"abstract_inverted_index":{"We":[0,46],"study":[1,28],"the":[2,20,33,36,41,67,84,89,107,125,129,142,153],"unique":[3],"information":[4,23],"function":[5,91],"U":[6,44,110],"I(T":[7,111],":":[8,112],"X":[9,72,113],"\\":[10,114],"Y":[11,74,115],")":[12],"defined":[13],"by":[14],"Bertschinger":[15],"et":[16],"al.":[17],"[4]":[18],"within":[19],"framework":[21],"of":[22,32,43,52,59,66,69,83,98,109,128,134,151],"decompositions.":[24],"In":[25,141],"particular,":[26],"we":[27,146],"uniqueness":[29],"and":[30,63,73],"support":[31,56],"solutions":[34,53,133],"to":[35,104],"convex":[37],"optimization":[38,130],"problem":[39],"underlying":[40],"definition":[42],"I.":[45],"identify":[47],"sufficient":[48],"conditions":[49,87],"for":[50],"non-uniqueness":[51],"with":[54],"full":[55],"in":[57,64,124],"terms":[58,65],"conditional":[60,99],"independence":[61],"constraints":[62,94],"cardinalities":[68],"T":[70,120,138],",":[71],".":[75],"Our":[76],"results":[77,102],"are":[78,132],"based":[79],"on":[80,88,95],"a":[81,96,148],"reformulation":[82],"first":[85],"order":[86],"objective":[90],"as":[92],"rank":[93],"matrix":[97],"probabilities.":[100],"These":[101],"help":[103],"speed":[105],"up":[106],"computation":[108],"),":[116],"most":[117],"notably":[118],"when":[119],"is":[121,139],"binary.":[122,140],"Optima":[123],"relative":[126],"interior":[127],"domain":[131],"linear":[135],"equations":[136],"if":[137],"all":[143],"binary":[144],"case,":[145],"obtain":[147],"complete":[149],"picture":[150],"where":[152],"optimizing":[154],"probability":[155],"distributions":[156],"lie.":[157]},"counts_by_year":[{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}