{"id":"https://openalex.org/W1968678581","doi":"https://doi.org/10.1145/1390156.1390242","title":"Efficiently solving convex relaxations for MAP estimation","display_name":"Efficiently solving convex relaxations for MAP estimation","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1968678581","doi":"https://doi.org/10.1145/1390156.1390242","mag":"1968678581"},"language":"en","primary_location":{"id":"doi:10.1145/1390156.1390242","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1390156.1390242","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 25th international conference on Machine learning - ICML '08","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":"https://openalex.org/A5018728658","display_name":"Manish Kumar","orcid":"https://orcid.org/0000-0002-1311-0976"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"M. Pawan Kumar","raw_affiliation_strings":["University of Oxford"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001534492","display_name":"Philip H. S. Torr","orcid":null},"institutions":[{"id":"https://openalex.org/I124261462","display_name":"Oxford Brookes University","ror":"https://ror.org/04v2twj65","country_code":"GB","type":"education","lineage":["https://openalex.org/I124261462"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"P. H. S. Torr","raw_affiliation_strings":["Oxford Brookes University","Oxford-Brookes University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oxford Brookes University","institution_ids":["https://openalex.org/I124261462"]},{"raw_affiliation_string":"Oxford-Brookes University","institution_ids":["https://openalex.org/I124261462"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.2285,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.97114932,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"680","last_page":"687"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9991000294685364,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9991000294685364,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.996999979019165,"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":0.9955000281333923,"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/submodular-set-function","display_name":"Submodular set function","score":0.5846100449562073},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5845699310302734},{"id":"https://openalex.org/keywords/maximum-a-posteriori-estimation","display_name":"Maximum a posteriori estimation","score":0.5646619200706482},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.45265406370162964},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44895753264427185},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44572460651397705},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4454183578491211},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4440302848815918},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.43896815180778503},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.4351329803466797},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.4223780632019043},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4152672290802002},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.33938083052635193},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.14249083399772644}],"concepts":[{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.5846100449562073},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5845699310302734},{"id":"https://openalex.org/C9810830","wikidata":"https://www.wikidata.org/wiki/Q635384","display_name":"Maximum a posteriori estimation","level":3,"score":0.5646619200706482},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.45265406370162964},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44895753264427185},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44572460651397705},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4454183578491211},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4440302848815918},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.43896815180778503},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.4351329803466797},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.4223780632019043},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4152672290802002},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.33938083052635193},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.14249083399772644},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1390156.1390242","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1390156.1390242","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 25th international conference on Machine learning - ICML '08","raw_type":"proceedings-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:23b59c06-76b5-445b-bf0a-d81c7f007b8a","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Conference item"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.7599999904632568,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1985123706","https://openalex.org/W2012605254","https://openalex.org/W2026820987","https://openalex.org/W2055636480","https://openalex.org/W2097525406","https://openalex.org/W2108619558","https://openalex.org/W2140789035","https://openalex.org/W2150675045","https://openalex.org/W2150734839","https://openalex.org/W2164918853","https://openalex.org/W2169551590","https://openalex.org/W2402851641"],"related_works":["https://openalex.org/W1595919516","https://openalex.org/W2945022594","https://openalex.org/W2142695913","https://openalex.org/W2039006033","https://openalex.org/W4236384091","https://openalex.org/W4382892785","https://openalex.org/W2169337137","https://openalex.org/W2015485697","https://openalex.org/W2012703063","https://openalex.org/W2097882228"],"abstract_inverted_index":{"The":[0],"problem":[1],"of":[2,10,16,22,38,51,65,123],"obtaining":[3],"the":[4,31,48,62,98,103,135,150],"maximum":[5],"a":[6,11,52,120],"posteriori":[7],"(MAP)":[8],"estimate":[9],"discrete":[12],"random":[13],"field":[14],"is":[15],"fundamental":[17],"importance":[18],"in":[19,106,147],"many":[20],"areas":[21],"Computer":[23],"Science.":[24],"In":[25],"this":[26],"work,":[27],"we":[28],"build":[29],"on":[30,119],"tree":[32],"reweighted":[33],"message":[34],"passing":[35],"(TRW)":[36],"framework":[37,152],"(Kolmogorov,":[39,107],"2006;":[40],"Wainwright":[41],"et":[42,88],"al.,":[43,89],"2005).":[44],"TRW":[45,66,151],"iteratively":[46],"optimizes":[47],"Lagrangian":[49],"dual":[50,63],"linear":[53],"programming":[54],"relaxation":[55],"for":[56,96,157],"MAP":[57,155],"estimation.":[58],"We":[59,91,115],"show":[60,133],"how":[61],"formulation":[64],"can":[67],"be":[68],"extended":[69],"to":[70,102,113],"include":[71],"cycle":[72,139],"inequalities":[73,140],"(Barahona":[74],"&":[75],"Mahjoub,":[76],"1986)":[77],"and":[78,141],"some":[79],"recently":[80],"proposed":[81],"second":[82],"order":[83],"cone":[84],"(SOC)":[85],"constraints":[86,137],"(Kumar":[87],"2007).":[90],"propose":[92],"efficient":[93],"iterative":[94],"algorithms":[95,110],"solving":[97],"resulting":[99],"duals.":[100],"Similar":[101],"method":[104],"described":[105],"2006),":[108],"these":[109],"are":[111],"guaranteed":[112],"converge.":[114],"test":[116],"our":[117],"approach":[118],"large":[121],"set":[122],"synthetic":[124],"data,":[125],"as":[126,128],"well":[127],"real":[129],"data.":[130],"Our":[131],"experiments":[132],"that":[134],"additional":[136],"(i.e.":[138],"SOC":[142],"constraints)":[143],"provide":[144],"better":[145],"results":[146],"cases":[148],"where":[149],"fails":[153],"(namely":[154],"estimation":[156],"non-submodular":[158],"energy":[159],"functions).":[160]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
