{"id":"https://openalex.org/W2155079033","doi":"https://doi.org/10.1109/tai.2003.1250231","title":"Approximate discrete probability distribution representation using a multi-resolution binary tree","display_name":"Approximate discrete probability distribution representation using a multi-resolution binary tree","publication_year":2004,"publication_date":"2004-03-02","ids":{"openalex":"https://openalex.org/W2155079033","doi":"https://doi.org/10.1109/tai.2003.1250231","mag":"2155079033"},"language":"en","primary_location":{"id":"doi:10.1109/tai.2003.1250231","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tai.2003.1250231","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 15th IEEE International Conference on Tools with Artificial Intelligence","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00068631","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025930086","display_name":"David Bellot","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"D. Bellot","raw_affiliation_strings":["Gravir/IMAG CNRS and INRIA Rh\u00f4ne-Alpes, Saint Ismier, France"],"affiliations":[{"raw_affiliation_string":"Gravir/IMAG CNRS and INRIA Rh\u00f4ne-Alpes, Saint Ismier, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025930086"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I1326498283"],"apc_list":null,"apc_paid":null,"fwci":2.3106,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.90009479,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"4","issue":null,"first_page":"498","last_page":"503"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9998999834060669,"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":0.9998999834060669,"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/T10906","display_name":"AI-based Problem Solving and Planning","score":0.9901000261306763,"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/T11106","display_name":"Data Management and Algorithms","score":0.9837999939918518,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"Joint probability distribution","score":0.7802199721336365},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.7116225361824036},{"id":"https://openalex.org/keywords/probability-mass-function","display_name":"Probability mass function","score":0.6775854825973511},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5680205821990967},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5545368790626526},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5266352295875549},{"id":"https://openalex.org/keywords/marginal-distribution","display_name":"Marginal distribution","score":0.5246415734291077},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.497847318649292},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.48981615900993347},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4763648509979248},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46865835785865784},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.466921329498291},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4382411241531372},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4329231381416321},{"id":"https://openalex.org/keywords/random-binary-tree","display_name":"Random binary tree","score":0.4194043278694153},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3529963791370392},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21398046612739563},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1387573778629303},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10699328780174255}],"concepts":[{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.7802199721336365},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.7116225361824036},{"id":"https://openalex.org/C197096303","wikidata":"https://www.wikidata.org/wiki/Q869887","display_name":"Probability mass function","level":3,"score":0.6775854825973511},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5680205821990967},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5545368790626526},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5266352295875549},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.5246415734291077},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.497847318649292},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.48981615900993347},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4763648509979248},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46865835785865784},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.466921329498291},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4382411241531372},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4329231381416321},{"id":"https://openalex.org/C11829167","wikidata":"https://www.wikidata.org/wiki/Q751292","display_name":"Random binary tree","level":3,"score":0.4194043278694153},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3529963791370392},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21398046612739563},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1387573778629303},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10699328780174255},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tai.2003.1250231","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tai.2003.1250231","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 15th IEEE International Conference on Tools with Artificial Intelligence","raw_type":"proceedings-article"},{"id":"pmh:oai:cogprints.org:3752","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401879","display_name":"CogPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Conference Paper"},{"id":"pmh:oai:HAL:hal-00068631v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00068631","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2003","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00068631v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00068631","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2003","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W89375548","https://openalex.org/W161081924","https://openalex.org/W1480376833","https://openalex.org/W1508405818","https://openalex.org/W1516111018","https://openalex.org/W1556084684","https://openalex.org/W1755360231","https://openalex.org/W1972676371","https://openalex.org/W1980343416","https://openalex.org/W2083719729","https://openalex.org/W2132020233","https://openalex.org/W2143891888","https://openalex.org/W2159080219","https://openalex.org/W2161051436","https://openalex.org/W2285295889","https://openalex.org/W3133236490","https://openalex.org/W4299515571","https://openalex.org/W6633452065"],"related_works":["https://openalex.org/W2951678044","https://openalex.org/W1510719821","https://openalex.org/W4300450359","https://openalex.org/W2117536196","https://openalex.org/W4234449911","https://openalex.org/W4243126796","https://openalex.org/W2753044481","https://openalex.org/W2122857041","https://openalex.org/W4245055104","https://openalex.org/W2042273572"],"abstract_inverted_index":{"Computing":[0],"and":[1,139,170],"storing":[2],"probabilities":[3],"is":[4,30,78,110,123,158],"a":[5,54,70,75,115,131,162],"hard":[6],"problem":[7,23,45],"as":[8,10],"soon":[9],"one":[11],"has":[12],"to":[13,82,130,150,161,171],"deal":[14],"with":[15,49],"complex":[16],"distributions":[17,29,52,95],"over":[18,53],"multiples":[19],"random":[20,57],"variables.":[21],"The":[22,43,141],"of":[24,27,34,40,56,100,114,118,137,144,166,175],"efficient":[25],"representation":[26,77,134,165,174],"probability":[28,51,65,112,168],"central":[31],"in":[32,37,80,135],"term":[33,136],"computational":[35],"efficiency":[36],"the":[38,101,105,108,111,121,124,148,153,167,176],"field":[39],"probabilistic":[41],"reasoning.":[42],"main":[44],"arises":[46],"when":[47],"dealing":[48],"joint":[50,87,94],"set":[55],"variables:":[58],"they":[59],"are":[60,147],"always":[61],"represented":[62],"using":[63,96],"huge":[64],"arrays.":[66],"In":[67],"this":[68],"paper,":[69],"new":[71],"method":[72],"based":[73],"on":[74],"binary-tree":[76],"introduced":[79],"order":[81],"store":[83],"efficiently":[84],"very":[85,132],"large":[86],"distributions.":[88],"Our":[89],"approach":[90,146],"approximates":[91],"any":[92],"multidimensional":[93],"an":[97,172],"adaptive":[98],"discretization":[99,125],"space.":[102],"We":[103],"make":[104],"assumption":[106,128],"that":[107],"lower":[109],"mass":[113],"particular":[116],"region":[117],"feature":[119],"space,":[120],"larger":[122],"step.":[126],"This":[127],"leads":[129],"optimized":[133],"time":[138,156],"memory.":[140],"other":[142],"advantages":[143],"our":[145],"ability":[149],"refine":[151],"dynamically":[152],"distribution":[154,169],"every":[155],"it":[157],"needed":[159],"leading":[160],"more":[163],"accurate":[164],"anytime":[173],"distribution.":[177]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}