{"id":"https://openalex.org/W4401692630","doi":"https://doi.org/10.1109/isit57864.2024.10619603","title":"The Bethe Partition Function and the SPA for Factor Graphs based on Homogeneous Real Stable Polynomials","display_name":"The Bethe Partition Function and the SPA for Factor Graphs based on Homogeneous Real Stable Polynomials","publication_year":2024,"publication_date":"2024-07-07","ids":{"openalex":"https://openalex.org/W4401692630","doi":"https://doi.org/10.1109/isit57864.2024.10619603"},"language":"en","primary_location":{"id":"doi:10.1109/isit57864.2024.10619603","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit57864.2024.10619603","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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":null,"display_name":"Yuwen Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yuwen Huang","raw_affiliation_strings":["The Chinese University of Hong Kong,Department of Information Engineering"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong,Department of Information Engineering","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028154201","display_name":"Pascal O. Vontobel","orcid":"https://orcid.org/0000-0002-6180-258X"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Pascal O. Vontobel","raw_affiliation_strings":["The Chinese University of Hong Kong,Department of Information Engineering"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong,Department of Information Engineering","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8671,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.84280792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"3029","last_page":"3034"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9404000043869019,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9404000043869019,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/homogeneous","display_name":"Homogeneous","score":0.7504911422729492},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5544405579566956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5322287678718567},{"id":"https://openalex.org/keywords/factor-graph","display_name":"Factor graph","score":0.4463749825954437},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.4316380023956299},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.4247950315475464},{"id":"https://openalex.org/keywords/factor","display_name":"Factor (programming language)","score":0.41955995559692383},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2867181599140167},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2616950571537018},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.24321633577346802},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22508841753005981},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16312113404273987},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12485584616661072},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06341713666915894}],"concepts":[{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.7504911422729492},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5544405579566956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5322287678718567},{"id":"https://openalex.org/C159246509","wikidata":"https://www.wikidata.org/wiki/Q5428725","display_name":"Factor graph","level":3,"score":0.4463749825954437},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.4316380023956299},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.4247950315475464},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.41955995559692383},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2867181599140167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2616950571537018},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.24321633577346802},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22508841753005981},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16312113404273987},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12485584616661072},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06341713666915894},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit57864.2024.10619603","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit57864.2024.10619603","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1560512119","https://openalex.org/W1594620223","https://openalex.org/W1997734382","https://openalex.org/W2006912660","https://openalex.org/W2008095352","https://openalex.org/W2075332134","https://openalex.org/W2086564526","https://openalex.org/W2137813581","https://openalex.org/W2139584447","https://openalex.org/W2142658489","https://openalex.org/W2150635973","https://openalex.org/W2150859678","https://openalex.org/W2160923591","https://openalex.org/W2169415915","https://openalex.org/W2563037975","https://openalex.org/W2566505556","https://openalex.org/W2761017552","https://openalex.org/W2920034339","https://openalex.org/W2971455278","https://openalex.org/W3103704874","https://openalex.org/W3138195762","https://openalex.org/W4229706427","https://openalex.org/W4234130962","https://openalex.org/W4250589301","https://openalex.org/W4293052541","https://openalex.org/W4299798129","https://openalex.org/W4307157081","https://openalex.org/W4392566520"],"related_works":["https://openalex.org/W162456724","https://openalex.org/W2354832544","https://openalex.org/W4252544247","https://openalex.org/W2903198223","https://openalex.org/W2137813581","https://openalex.org/W4288388634","https://openalex.org/W4294567731","https://openalex.org/W2808407214","https://openalex.org/W1557056212","https://openalex.org/W2757251458"],"abstract_inverted_index":{"Various":[0],"computational":[1],"problems":[2],"can":[3,98],"be":[4,99],"reduced":[5],"to":[6],"computing":[7,137],"the":[8,11,37,57,64,71,78,82,85,92,96,141,146,173,180,183,189,198,214,227,232,236,242,253,257,270,273,276],"marginals":[9],"and":[10,77,144,158,206],"partition":[12,54,185,190,278],"function":[13,55,68,76,115,186,246,279],"of":[14,41,59,84,95,109,130,140,148,165,172,200,216,226,235,238,265,275],"a":[15,60,74,107,120,138,161,223],"suitably":[16],"defined":[17,117],"standard":[18],"factor":[19],"graph":[20],"(S-FG).":[21],"The":[22],"sum-product":[23],"algorithm":[24],"(SPA)":[25],"is":[26,73,116],"an":[27,51,260],"efficient":[28],"iterative":[29],"method":[30],"for":[31,50,160,202,213,252],"approximating":[32],"these":[33,42,177],"quantities,":[34],"resulting":[35],"in":[36],"so-called":[38],"Bethe":[39,65,86,93,184,243,277],"approximation":[40,94],"quantities.":[43],"In":[44,192],"previous":[45],"work,":[46],"Vontobel":[47],"proved":[48],"that":[49,176,182,222,241,269],"S-FG":[52,72,258],"whose":[53],"equals":[56,231],"permanent":[58,97,143],"nonnegative":[61],"square":[62],"matrix,":[63],"free":[66,87,244],"energy":[67,88,245],"associated":[69],"with":[70,152,197],"convex":[75,233],"SPA":[79,261,271],"efficiently":[80],"finds":[81,272],"minimum":[83],"function,":[89],"from":[90,208],"which":[91],"computed.":[100],"We":[101],"extend":[102],"Vontobel's":[103],"results":[104,201,207],"by":[105,156],"considering":[106],"class":[108,129,164,215],"bipartite":[110],"S-FGs":[111,131,166,178,217],"where":[112,256],"each":[113],"local":[114,228],"based":[118],"on":[119],"(possibly":[121],"different)":[122],"multi-affine":[123],"homogeneous":[124],"real":[125,203],"stable":[126,204],"polynomial.":[127],"This":[128],"covers":[132],"various":[133,211],"combinatorial":[134],"problems,":[135],"including":[136],"generalization":[139],"matrix":[142],"determining":[145],"number":[147],"binary":[149],"contingency":[150],"tables":[151],"prescribed":[153],"marginals.":[154],"Results":[155],"Straszak":[157],"Vishnoi":[159],"slightly":[162],"larger":[163],"(they":[167],"do":[168],"not":[169],"assume":[170],"homogeneity":[171],"polynomials)":[174],"show":[175,221],"have":[179],"property":[181],"lower":[187],"bounds":[188],"function.":[191],"this":[193],"paper":[194],"we":[195,220],"prove,":[196],"help":[199],"polynomials":[205],"matroid":[209],"theory,":[210],"statements":[212],"under":[218],"consideration:":[219],"certain":[224],"projection":[225],"marginal":[229],"polytope":[230],"hull":[234],"set":[237],"valid":[239],"configurations,":[240],"possesses":[247],"some":[248],"convexity":[249],"properties,":[250],"and,":[251],"typical":[254],"case":[255],"has":[259],"fixed":[262],"point":[263],"consisting":[264],"positive-valued":[266],"messages":[267],"only,":[268],"value":[274],"exponentially":[280],"fast.":[281]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
