{"id":"https://openalex.org/W7128615816","doi":"https://doi.org/10.48550/arxiv.2602.09711","title":"Directed Information: Estimation, Optimization and Applications in Communications and Causality","display_name":"Directed Information: Estimation, Optimization and Applications in Communications and Causality","publication_year":2026,"publication_date":"2026-02-10","ids":{"openalex":"https://openalex.org/W7128615816","doi":"https://doi.org/10.48550/arxiv.2602.09711"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.09711","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.09711","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.09711","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077599107","display_name":"Dor Tsur","orcid":"https://orcid.org/0000-0002-6561-4965"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tsur, Dor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087127628","display_name":"Oron Sabag","orcid":"https://orcid.org/0000-0002-7907-1463"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sabag, Oron","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059452861","display_name":"Navin Kashyap","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kashyap, Navin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068879871","display_name":"Haim H. Permuter","orcid":"https://orcid.org/0000-0003-3170-3190"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Permuter, Haim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125669385","display_name":"Gerhard Kramer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kramer, Gerhard","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":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13553","display_name":"Age of Information Optimization","score":0.5521000027656555,"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/T13553","display_name":"Age of Information Optimization","score":0.5521000027656555,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.17880000174045563,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.06870000064373016,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6593000292778015},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.6593000292778015},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.6419000029563904},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5081999897956848},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5058000087738037},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.48500001430511475},{"id":"https://openalex.org/keywords/conditional-independence","display_name":"Conditional independence","score":0.4442000091075897},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.44200000166893005},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.42100000381469727},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.39809998869895935}],"concepts":[{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.6593000292778015},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6593000292778015},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.6419000029563904},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5081999897956848},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5080000162124634},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5058000087738037},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.48500001430511475},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.4442000091075897},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.44200000166893005},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.42100000381469727},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.39809998869895935},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3950999975204468},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3926999866962433},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.37380000948905945},{"id":"https://openalex.org/C8854915","wikidata":"https://www.wikidata.org/wiki/Q4350200","display_name":"Information transfer","level":2,"score":0.3727000057697296},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.36890000104904175},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C123197309","wikidata":"https://www.wikidata.org/wiki/Q2882343","display_name":"Multi-armed bandit","level":3,"score":0.34790000319480896},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.34290000796318054},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.34119999408721924},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33730000257492065},{"id":"https://openalex.org/C2779136372","wikidata":"https://www.wikidata.org/wiki/Q10283002","display_name":"Information flow","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C124805900","wikidata":"https://www.wikidata.org/wiki/Q5159269","display_name":"Conditional mutual information","level":3,"score":0.2797999978065491},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C2778153524","wikidata":"https://www.wikidata.org/wiki/Q4241335","display_name":"Optimality criterion","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.09711","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.09711","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.09711","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.09711","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Directed":[0],"information":[1,5,16,54],"(DI)":[2],"is":[3,24,135,174,188,195,214],"an":[4,45,220],"measure":[6],"that":[7,270],"attempts":[8],"to":[9,21,27,80,98,137,139,168,233,237,263],"capture":[10],"directionality":[11],"in":[12,53],"the":[13,58,70,103,133,141,157,160,164,169,177,186,192,202,206,211,215,245,259],"flow":[14],"of":[15,47,60,72,89,105,121,132,144,151,159,179,201,219,248],"from":[17,94,163,258],"one":[18],"random":[19],"process":[20,167,225],"another.":[22],"It":[23],"closely":[25],"related":[26],"other":[28],"causal":[29,40,180],"influence":[30],"measures,":[31],"such":[32,112],"as":[33],"transfer":[34],"entropy,":[35],"Granger":[36],"causality,":[37],"and":[38,49,64,77,126,205,266,275],"Pearl's":[39],"framework.":[41],"This":[42,172,227,252],"monograph":[43,134,253],"provides":[44],"overview":[46],"DI":[48,90,116,161],"its":[50,74,78],"main":[51],"application":[52,104],"theory,":[55],"namely,":[56],"characterizing":[57],"capacity":[59,107,143,150,213,247],"channels":[61,146],"with":[62],"feedback":[63,142,149,212,246],"memory.":[65],"We":[66],"begin":[67],"by":[68,197],"reviewing":[69],"definitions":[71],"DI,":[73],"basic":[75],"properties,":[76],"relation":[79],"Shannon's":[81],"mutual":[82],"information.":[83],"Next,":[84],"we":[85,109],"provide":[86],"a":[87,119,152,198,249],"survey":[88],"estimation":[91],"techniques,":[92],"ranging":[93],"classic":[95],"plug-in":[96],"estimators":[97,113],"modern":[99],"neural-network-based":[100],"estimators.":[101],"Considering":[102],"channel":[106,165],"estimation,":[108],"describe":[110],"how":[111],"numerically":[114],"optimize":[115],"rate":[117,162],"over":[118,176],"class":[120,178],"joint":[122],"distributions":[123],"on":[124],"input":[125,166,183,274],"output":[127,170,276],"processes.":[128],"A":[129],"significant":[130],"part":[131],"devoted":[136],"techniques":[138],"compute":[140,238],"finite-state":[145],"(FSCs).":[147],"The":[148],"strongly":[153],"connected":[154],"FSC":[155,187],"involves":[156],"maximization":[158,173],"process.":[171],"performed":[175],"conditioned":[181],"probability":[182],"distributions.":[184],"When":[185],"also":[189],"unifilar,":[190],"i.e.,":[191],"next":[193],"state":[194,204],"given":[196],"time-invariant":[199],"function":[200],"current":[203],"new":[207],"input-output":[208],"symbol":[209],"pair,":[210],"optimal":[216],"average":[217],"reward":[218],"appropriately":[221],"formulated":[222],"Markov":[223],"decision":[224],"(MDP).":[226],"MDP":[228],"formulation":[229],"has":[230],"been":[231],"exploited":[232],"develop":[234],"several":[235],"methods":[236],"exactly,":[239],"or":[240],"at":[241],"least":[242],"estimate":[243],"closely,":[244],"unifilar":[250],"FSC.":[251],"describes":[254],"these":[255],"methods,":[256,265],"starting":[257],"value":[260],"iteration":[261],"algorithm,":[262],"Q-graph":[264],"reinforcement":[267],"learning":[268],"algorithms":[269],"can":[271],"handle":[272],"large":[273],"alphabets.":[277]},"counts_by_year":[],"updated_date":"2026-08-16T07:02:28.622633","created_date":"2026-02-12T00:00:00"}
