{"id":"https://openalex.org/W2130697955","doi":"https://doi.org/10.1109/tit.2010.2079014","title":"Norm-Product Belief Propagation: Primal-Dual Message-Passing for Approximate Inference","display_name":"Norm-Product Belief Propagation: Primal-Dual Message-Passing for Approximate Inference","publication_year":2010,"publication_date":"2010-11-30","ids":{"openalex":"https://openalex.org/W2130697955","doi":"https://doi.org/10.1109/tit.2010.2079014","mag":"2130697955"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2010.2079014","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2079014","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000106487","display_name":"Tamir Hazan","orcid":"https://orcid.org/0000-0003-1652-3845"},"institutions":[{"id":"https://openalex.org/I160992636","display_name":"Toyota Technological Institute at Chicago","ror":"https://ror.org/02sn5gb64","country_code":"US","type":"education","lineage":["https://openalex.org/I160992636"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tamir Hazan","raw_affiliation_strings":["Toyota Institute of Technology, Chicago, IL, USA","TTI, Chicago, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Toyota Institute of Technology, Chicago, IL, USA","institution_ids":["https://openalex.org/I160992636"]},{"raw_affiliation_string":"TTI, Chicago, IL, USA","institution_ids":["https://openalex.org/I160992636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075004917","display_name":"Amnon Shashua","orcid":null},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Amnon Shashua","raw_affiliation_strings":["School of Engineering and Computer Science, Hebrew University of Jerusalem, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Computer Science, Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":17.0222,"has_fulltext":false,"cited_by_count":103,"citation_normalized_percentile":{"value":0.99176377,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"56","issue":"12","first_page":"6294","last_page":"6316"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9986000061035156,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9927999973297119,"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/belief-propagation","display_name":"Belief propagation","score":0.5791224241256714},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5198781490325928},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4368019700050354},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.43440601229667664},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41331225633621216},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40280407667160034},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3770264983177185},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3263995349407196},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32616370916366577},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2669801712036133}],"concepts":[{"id":"https://openalex.org/C152948882","wikidata":"https://www.wikidata.org/wiki/Q4060686","display_name":"Belief propagation","level":3,"score":0.5791224241256714},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5198781490325928},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4368019700050354},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.43440601229667664},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41331225633621216},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40280407667160034},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3770264983177185},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3263995349407196},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32616370916366577},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2669801712036133},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","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":1,"locations":[{"id":"doi:10.1109/tit.2010.2079014","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2079014","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.7799999713897705}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":93,"referenced_works":["https://openalex.org/W1502653686","https://openalex.org/W1528845765","https://openalex.org/W1530042113","https://openalex.org/W1563704153","https://openalex.org/W1583497301","https://openalex.org/W1599270913","https://openalex.org/W1601035521","https://openalex.org/W1746680969","https://openalex.org/W1828211540","https://openalex.org/W1829360078","https://openalex.org/W1875056259","https://openalex.org/W1891202952","https://openalex.org/W1936569394","https://openalex.org/W1957358235","https://openalex.org/W1964938049","https://openalex.org/W1970851820","https://openalex.org/W1991133427","https://openalex.org/W2007995670","https://openalex.org/W2010495720","https://openalex.org/W2022393739","https://openalex.org/W2033468335","https://openalex.org/W2039050532","https://openalex.org/W2041815422","https://openalex.org/W2047408445","https://openalex.org/W2050958540","https://openalex.org/W2089770904","https://openalex.org/W2099091355","https://openalex.org/W2099997071","https://openalex.org/W2100034662","https://openalex.org/W2101478306","https://openalex.org/W2105934661","https://openalex.org/W2108619558","https://openalex.org/W2115166723","https://openalex.org/W2118696796","https://openalex.org/W2121606987","https://openalex.org/W2124541940","https://openalex.org/W2128765501","https://openalex.org/W2130178369","https://openalex.org/W2131538180","https://openalex.org/W2135094946","https://openalex.org/W2135414191","https://openalex.org/W2137813581","https://openalex.org/W2141155330","https://openalex.org/W2143524933","https://openalex.org/W2144306116","https://openalex.org/W2149474573","https://openalex.org/W2149760002","https://openalex.org/W2150218618","https://openalex.org/W2150675045","https://openalex.org/W2150734839","https://openalex.org/W2153745131","https://openalex.org/W2158863086","https://openalex.org/W2159080219","https://openalex.org/W2160709761","https://openalex.org/W2161246326","https://openalex.org/W2164918853","https://openalex.org/W2169282664","https://openalex.org/W2169415915","https://openalex.org/W2169447051","https://openalex.org/W2175160295","https://openalex.org/W2564555264","https://openalex.org/W2582449852","https://openalex.org/W2799004609","https://openalex.org/W2807232057","https://openalex.org/W2952346284","https://openalex.org/W2963217435","https://openalex.org/W2987657883","https://openalex.org/W3004177386","https://openalex.org/W3103862435","https://openalex.org/W3141595720","https://openalex.org/W3141717690","https://openalex.org/W4232449707","https://openalex.org/W4249667877","https://openalex.org/W4300188436","https://openalex.org/W4301259139","https://openalex.org/W6631513056","https://openalex.org/W6633670269","https://openalex.org/W6635752617","https://openalex.org/W6636093472","https://openalex.org/W6637407456","https://openalex.org/W6638725582","https://openalex.org/W6639344520","https://openalex.org/W6639619815","https://openalex.org/W6640150328","https://openalex.org/W6640992714","https://openalex.org/W6674884877","https://openalex.org/W6675196758","https://openalex.org/W6681274554","https://openalex.org/W6681421934","https://openalex.org/W6682199522","https://openalex.org/W6683341419","https://openalex.org/W6683830501","https://openalex.org/W6752562311"],"related_works":["https://openalex.org/W2963817320","https://openalex.org/W2377432969","https://openalex.org/W4307680413","https://openalex.org/W2396038226","https://openalex.org/W2109489568","https://openalex.org/W2949726649","https://openalex.org/W2096464203","https://openalex.org/W3003852655","https://openalex.org/W4226280974","https://openalex.org/W4300477075"],"abstract_inverted_index":{"Inference":[0],"problems":[1],"in":[2],"graphical":[3],"models":[4],"can":[5],"be":[6,211],"represented":[7],"as":[8,82,240,250],"a":[9,13,40,69,83,86,97],"constrained":[10],"optimization":[11,117,163,181],"of":[12,23,29,54,72,85,91,152,164,192,222,235,243],"free-energy":[14],"function.":[15],"In":[16,45],"this":[17,92],"paper,":[18],"we":[19,47,247],"treat":[20],"both":[21],"forms":[22],"probabilistic":[24],"inference,":[25],"estimating":[26],"marginal":[27,223],"probabilities":[28,224],"the":[30,35,49,101,115,120,129,144,153,165,172,180,186,193,206,214,220,228,236,241,244,251,263],"joint":[31],"distribution":[32],"and":[33,56,58,62,67,78,104,128,158,184,197,202,225,259],"finding":[34],"most":[36],"probable":[37],"assignment,":[38],"through":[39],"unified":[41],"message-passing":[42,188],"algorithm":[43,147],"architecture.":[44],"particular":[46],"generalize":[48],"belief":[50],"propagation":[51],"(BP)":[52],"algorithms":[53,65,74,106],"sum-product":[55,196],"max-product":[57,198],"tree-reweighted":[59],"(TRW)":[60],"sum":[61],"max":[63],"product":[64],"(TRBP)":[66],"introduce":[68,185,232],"new":[70],"set":[71,209],"convergent":[73,218,256],"based":[75],"on":[76,100],"\u201cconvex-free-energy\u201d":[77],"linear-programming":[79],"(LP)":[80],"relaxation":[81],"zero-temperature":[84],"convex-free-energy.":[87],"The":[88,253],"main":[89],"idea":[90],"work":[93],"arises":[94,239],"from":[95,114,139],"taking":[96],"general":[98,166],"perspective":[99],"existing":[102],"BP":[103],"TRBP":[105,201],"while":[107],"observing":[108],"that":[109],"they":[110],"all":[111],"are":[112],"reductions":[113],"basic":[116],"formula":[118,182],"off+\u03a3ihiwhere":[119],"functionfis":[121],"an":[122,150],"extended-valued,":[123],"strictly":[124],"convex":[125,140,212],"but":[126],"nonsmooth":[127],"functionshiare":[130],"extended-valued":[131],"functions":[132],"(not":[133],"necessarily":[134],"convex).":[135],"We":[136,169,230],"use":[137],"tools":[138],"duality":[141],"to":[142,161,210,249],"present":[143],"\u201cprimal-dual":[145],"ascent\u201d":[146],"which":[148,238,246],"is":[149,159,208,216,255],"extension":[151],"Bregman":[154],"successive":[155],"projection":[156],"scheme":[157],"designed":[160],"handle":[162],"typef+":[167],"\u03a3ihi.":[168],"then":[170],"map":[171],"fractional-free-energy":[173,207],"variational":[174],"principle":[175],"for":[176,219,226],"approximate":[177],"inference":[178],"onto":[179],"above":[183],"\u201cnorm-product\u201d":[187],"algorithm.":[189],"Special":[190],"cases":[191],"norm-product":[194,215,237],"include":[195],"(BP":[199],"algorithms),":[200],"NMPLP":[203],"algorithms.":[204],"When":[205],"(convex-free-energy)":[213],"globally":[217],"estimation":[221],"approximating":[227],"LP-relaxation.":[229],"also":[231],"another":[233],"branch":[234],"\u201czero-temperature\u201d":[242],"convex-free-energy":[245],"refer":[248],"\u201cconvex-max-product\u201d.":[252],"convex-max-product":[254],"(unlike":[257],"max-product)":[258],"aims":[260],"at":[261],"solving":[262],"LP-":[264],"relaxation.":[265]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":17}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
