{"id":"https://openalex.org/W7100106963","doi":null,"title":"Addendum to \u201cStructured Region Graphs: Morphing EP into GBP\u201d","display_name":"Addendum to \u201cStructured Region Graphs: Morphing EP into GBP\u201d","publication_year":2014,"publication_date":"2014-02-04","ids":{"openalex":"https://openalex.org/W7100106963"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.420.8308","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.420.8308","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ics.uci.edu/~welling/publications/papers/AddendumUAI05-v2.pdf","raw_type":"text"},"volume":null,"type":"article","indexed_in":[],"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/A5087368991","display_name":"Max Welling","orcid":"https://orcid.org/0000-0003-1484-2121","observed_orcids":["https://orcid.org/0000-0003-1484-2121"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Max Welling","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064373793","display_name":"Yee Whye Teh","orcid":"https://orcid.org/0000-0001-5365-6933","observed_orcids":["https://orcid.org/0000-0001-5365-6933"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yee Whye Teh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111929449","display_name":"Thomas P. Minka","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas P. Minka","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Reduction Rules","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reduction Rules","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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.62000913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9970999956130981,"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":0.9970999956130981,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.0003000000142492354,"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/gbp","display_name":"GBP","score":0.44600000977516174},{"id":"https://openalex.org/keywords/ep","display_name":"EP","score":0.49399998784065247},{"id":"https://openalex.org/keywords/belief-propagation","display_name":"belief propagation","score":0.5320000052452087},{"id":"https://openalex.org/keywords/natural-numbers","display_name":"natural numbers","score":0.6169999837875366},{"id":"https://openalex.org/keywords/free-energy","display_name":"free energy","score":0.5759999752044678},{"id":"https://openalex.org/keywords/fixed-points","display_name":"fixed points","score":0.8529999852180481},{"id":"https://openalex.org/keywords/factor-graphs","display_name":"factor graphs","score":0.4779999852180481},{"id":"https://openalex.org/keywords/message-passing","display_name":"message passing","score":0.6060000061988831},{"id":"https://openalex.org/keywords/dirac-delta-function","display_name":"Dirac delta function","score":0.38600000739097595}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.666700005531311},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6639999747276306},{"id":"https://openalex.org/C201811572","wikidata":"https://www.wikidata.org/wiki/Q188518","display_name":"Descendant","level":2,"score":0.6542999744415283},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.571399986743927},{"id":"https://openalex.org/C2778945725","wikidata":"https://www.wikidata.org/wiki/Q352858","display_name":"Addendum","level":2,"score":0.5354999899864197},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4740999937057495},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4429999887943268},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.42480000853538513},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.3125},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C50637493","wikidata":"https://www.wikidata.org/wiki/Q1136781","display_name":"Morphing","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.420.8308","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.420.8308","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ics.uci.edu/~welling/publications/papers/AddendumUAI05-v2.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7095297429","https://openalex.org/W2949670190","https://openalex.org/W7096131641","https://openalex.org/W2132087991","https://openalex.org/W2169415915","https://openalex.org/W2901989896","https://openalex.org/W2108818808","https://openalex.org/W7097148675","https://openalex.org/W4310902978","https://openalex.org/W7099231131"],"abstract_inverted_index":{"These":[0],"rules":[1,9],"represent":[2],"generalizations":[3,35],"of":[4,8,23,28,36,50,54,71,113,121,161,206,213,220,272,281,292,299,335,352],"a":[5,69,119,204,211,251,269,296,308,321,333,339,349],"similar":[6],"set":[7,334],"for":[10,17],"RGs":[11],"introduced":[12],"in":[13,75,86,354,386],"[3].":[14],"The":[15,238],"proofs":[16,38],"conditions":[18],"C1,":[19],"C2,":[20],"C3,":[21],"conservation":[22],"counting":[24,232,282],"numbers":[25,165],"and":[26,59,73,99,105,115,135,146,154,169,208,240,302],"equivalence":[27],"the":[29,37,51,55,76,79,162,174,226,230,254,279,285,293,300,383],"(constrained)":[30],"free":[31,246,286],"energy":[32,247],"are":[33,61,225,257,364,372],"straightforward":[34],"presented":[39],"there":[40],"or":[41,218],"easily":[42,62],"checked.":[43],"Below":[44],"we":[45],"focus":[46],"on":[47,276],"proving":[48],"some":[49],"necessary":[52],"properties":[53],"split":[56],"move":[57],"(C1":[58],"C2":[60],"checked).":[63],"First":[64],"note":[65],"that":[66,78,332,378],"S":[67,102,108,134,139,145,149,155,168,172,267],"is":[68,140,209,268,295,315,348,380],"separator":[70,271],"A":[72,100,104,114,132,143,166],"B":[74,106,116,136,147,170],"sense":[77],"variables":[80,344],"xS":[81],"separate":[82],"xA":[83],"from":[84],"xB":[85],"G(R).":[87,273],"C3":[88],"(hierarchy)":[89],"If":[90,307],"R":[91,128,178,207],"has":[92,96,229,311,320],"parents,":[93],"then":[94,129,318,367],"it":[95],"no":[97],"factors":[98],"\u222a":[101,107,133,137,144,148,167,171],"=":[103,109,181,183,187,197,264],"B.":[110],"Every":[111],"clique":[112,120],"was":[117,203],"once":[118],"R,":[122],"so":[123,179],"if":[124,360],"R\u2019s":[125],"parents":[126],"subsumed":[127,141],"they":[130],"subsume":[131,156],"S.":[138],"by":[142,150,159,259],"definition.":[151],"A,":[152,215],"B,":[153,217,222],"their":[157],"children":[158],"definition":[160],"construction.":[163],"Counting":[164],"have":[173,244],"same":[175,231],"ancestors":[176],"as":[177,234],"cA":[180,194],"cB":[182],"cR.":[184],"Furthermore":[185],"cS":[186],"1":[188],"\u2212":[189,191],"((1":[190],"cR)":[192],"+":[193,195],"cB)":[196],"\u2212cR.":[198],"Thus":[199],"any":[200,368],"region":[201,242,255],"which":[202,261],"descendant":[205,212],"now":[210],"only":[214,216,227,338],"all":[219,343,361],"(A,":[221],"S)":[223],"(these":[224],"possibilities)":[228],"number":[233],"before.":[235],"Fixed":[236],"points":[237],"old":[239,294],"new":[241],"graphs":[243],"different":[245],"functions.":[248,375],"However,":[249],"at":[250],"fixed":[252,290,297,322,350],"point,":[253],"beliefs":[256,336],"given":[258],"Eqn.8,":[260],"means":[262],"qR(xR)":[263],"qA(xA)qB(xB)/qS(xS)":[265],"since":[266],"complete":[270],"This":[274],"condition":[275],"qR,":[277],"plus":[278],"equality":[280],"numbers,":[283],"makes":[284],"energies":[287],"equivalent.":[288],"Any":[289],"point":[291,298,323,351],"new,":[301],"vice":[303],"versa.":[304],"Theorem":[305],"4":[306],"factorless":[309],"RG":[310],"inner":[312],"regions":[313],"yet":[314],"not":[316],"reducible,":[317],"GBP":[319,353],"other":[324,358],"than":[325],"uniform":[326],"beliefs.":[327],"Proof:":[328],"We":[329],"will":[330],"show":[331],"allowing":[337],"single":[340],"state,":[341],"say":[342],"equal":[345],"to":[346],"1,":[347],"this":[355,379],"case.":[356],"In":[357],"words,":[359],"existing":[362],"messages":[363,371],"delta":[365,374],"functions,":[366],"newly":[369],"computed":[370],"also":[373],"To":[376],"see":[377],"true,":[381],"consider":[382],"message":[384],"equation":[385]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-27T00:00:00"}