{"id":"https://openalex.org/W2114267799","doi":"https://doi.org/10.7916/d8xg9z41","title":"Learning with Degree-Based Subgraph Estimation","display_name":"Learning with Degree-Based Subgraph Estimation","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2114267799","doi":"https://doi.org/10.7916/d8xg9z41","mag":"2114267799"},"language":"en","primary_location":{"id":"pmh:oai:academiccommons.columbia.edu:10.7916/D8XG9Z41","is_oa":false,"landing_page_url":"https://doi.org/10.7916/D8XG9Z41","pdf_url":null,"source":{"id":"https://openalex.org/S4306402601","display_name":"Columbia Academic Commons (Columbia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I78577930","host_organization_name":"Columbia University","host_organization_lineage":["https://openalex.org/I78577930"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Theses"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.7916/d8xg9z41","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Huang, Bert","orcid":null},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Huang, Bert","raw_affiliation_strings":["Columbia University"],"affiliations":[{"raw_affiliation_string":"Columbia University","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12858089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"162","last_page":"162"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9979000091552734,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.9979000091552734,"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":0.9966999888420105,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/belief-propagation","display_name":"Belief propagation","score":0.5747929215431213},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5406164526939392},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"Degree distribution","score":0.5365298986434937},{"id":"https://openalex.org/keywords/graphical-model","display_name":"Graphical model","score":0.5138381123542786},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4905771315097809},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.48776012659072876},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.47745636105537415},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4733978509902954},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.444853276014328},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4343947470188141},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.43284517526626587},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.42171812057495117},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4180288016796112},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41217291355133057},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37832316756248474},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37380528450012207},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28325700759887695},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.22493493556976318}],"concepts":[{"id":"https://openalex.org/C152948882","wikidata":"https://www.wikidata.org/wiki/Q4060686","display_name":"Belief propagation","level":3,"score":0.5747929215431213},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5406164526939392},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.5365298986434937},{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.5138381123542786},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4905771315097809},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.48776012659072876},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.47745636105537415},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4733978509902954},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.444853276014328},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4343947470188141},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.43284517526626587},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42171812057495117},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4180288016796112},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41217291355133057},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37832316756248474},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37380528450012207},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28325700759887695},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.22493493556976318},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:academiccommons.columbia.edu:10.7916/D8XG9Z41","is_oa":false,"landing_page_url":"https://doi.org/10.7916/D8XG9Z41","pdf_url":null,"source":{"id":"https://openalex.org/S4306402601","display_name":"Columbia Academic Commons (Columbia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I78577930","host_organization_name":"Columbia University","host_organization_lineage":["https://openalex.org/I78577930"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Theses"},{"id":"mag:2114267799","is_oa":false,"landing_page_url":"http://people.cs.vt.edu/~bhuang/papers/BertHuangThesis.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null},{"id":"doi:10.7916/d8xg9z41","is_oa":true,"landing_page_url":"https://doi.org/10.7916/d8xg9z41","pdf_url":null,"source":{"id":"https://openalex.org/S4306402601","display_name":"Columbia Academic Commons (Columbia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I78577930","host_organization_name":"Columbia University","host_organization_lineage":["https://openalex.org/I78577930"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.7916/d8xg9z41","is_oa":true,"landing_page_url":"https://doi.org/10.7916/d8xg9z41","pdf_url":null,"source":{"id":"https://openalex.org/S4306402601","display_name":"Columbia Academic Commons (Columbia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I78577930","host_organization_name":"Columbia University","host_organization_lineage":["https://openalex.org/I78577930"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":119,"referenced_works":["https://openalex.org/W78511820","https://openalex.org/W119677570","https://openalex.org/W120301130","https://openalex.org/W641132676","https://openalex.org/W1485617437","https://openalex.org/W1500353311","https://openalex.org/W1502916507","https://openalex.org/W1528845765","https://openalex.org/W1532499126","https://openalex.org/W1552347772","https://openalex.org/W1572931153","https://openalex.org/W1574662932","https://openalex.org/W1627947145","https://openalex.org/W1628027163","https://openalex.org/W1629473008","https://openalex.org/W1662487404","https://openalex.org/W1718512272","https://openalex.org/W1761820742","https://openalex.org/W1792316426","https://openalex.org/W1860880244","https://openalex.org/W1880262756","https://openalex.org/W1966139704","https://openalex.org/W1969357318","https://openalex.org/W1970493189","https://openalex.org/W1974778955","https://openalex.org/W1976618413","https://openalex.org/W1981020230","https://openalex.org/W1985749074","https://openalex.org/W1986065347","https://openalex.org/W1991728994","https://openalex.org/W1995990042","https://openalex.org/W1999848117","https://openalex.org/W2000157792","https://openalex.org/W2005126631","https://openalex.org/W2006912660","https://openalex.org/W2027752285","https://openalex.org/W2031248101","https://openalex.org/W2035720976","https://openalex.org/W2037576616","https://openalex.org/W2037933327","https://openalex.org/W2044105411","https://openalex.org/W2045656233","https://openalex.org/W2047408445","https://openalex.org/W2054141820","https://openalex.org/W2057175746","https://openalex.org/W2059608229","https://openalex.org/W2061212083","https://openalex.org/W2073792299","https://openalex.org/W2084809122","https://openalex.org/W2085040216","https://openalex.org/W2087551996","https://openalex.org/W2089770904","https://openalex.org/W2094414211","https://openalex.org/W2099091355","https://openalex.org/W2103860820","https://openalex.org/W2106053110","https://openalex.org/W2107107106","https://openalex.org/W2110325612","https://openalex.org/W2112681514","https://openalex.org/W2115166723","https://openalex.org/W2116440993","https://openalex.org/W2117354486","https://openalex.org/W2118696796","https://openalex.org/W2118997898","https://openalex.org/W2119384858","https://openalex.org/W2119605717","https://openalex.org/W2120295426","https://openalex.org/W2120340025","https://openalex.org/W2122090912","https://openalex.org/W2123114526","https://openalex.org/W2124637492","https://openalex.org/W2124672527","https://openalex.org/W2125993116","https://openalex.org/W2131951207","https://openalex.org/W2135838082","https://openalex.org/W2137207609","https://openalex.org/W2137245235","https://openalex.org/W2139688603","https://openalex.org/W2139823104","https://openalex.org/W2141461755","https://openalex.org/W2141923507","https://openalex.org/W2142623206","https://openalex.org/W2142887429","https://openalex.org/W2144414892","https://openalex.org/W2144730813","https://openalex.org/W2148727093","https://openalex.org/W2149580580","https://openalex.org/W2150760714","https://openalex.org/W2151052953","https://openalex.org/W2151933617","https://openalex.org/W2154455818","https://openalex.org/W2155912844","https://openalex.org/W2158535911","https://openalex.org/W2159080219","https://openalex.org/W2160268549","https://openalex.org/W2160392814","https://openalex.org/W2161055874","https://openalex.org/W2161611531","https://openalex.org/W2164424155","https://openalex.org/W2165558283","https://openalex.org/W2169015768","https://openalex.org/W2169038197","https://openalex.org/W2169415915","https://openalex.org/W2169600004","https://openalex.org/W2170682041","https://openalex.org/W2170987079","https://openalex.org/W2175160295","https://openalex.org/W2289549408","https://openalex.org/W2310919327","https://openalex.org/W2398757277","https://openalex.org/W2535123820","https://openalex.org/W2743803189","https://openalex.org/W2807232057","https://openalex.org/W2973651390","https://openalex.org/W2989661724","https://openalex.org/W3104833085","https://openalex.org/W3120740533","https://openalex.org/W3125564681","https://openalex.org/W3145128584"],"related_works":["https://openalex.org/W2307775862","https://openalex.org/W3196170424","https://openalex.org/W3021801498","https://openalex.org/W3013329596","https://openalex.org/W2912077575","https://openalex.org/W3198001881","https://openalex.org/W3104683355","https://openalex.org/W1647260487","https://openalex.org/W3099179075","https://openalex.org/W2971920121","https://openalex.org/W1973938657","https://openalex.org/W3208212828","https://openalex.org/W2900216709","https://openalex.org/W3033495140","https://openalex.org/W2549095393","https://openalex.org/W2998008360","https://openalex.org/W2996300530","https://openalex.org/W2922924332","https://openalex.org/W2153007951","https://openalex.org/W3161315274"],"abstract_inverted_index":{"Networks":[0],"and":[1,19,30,46,92,180,227,250,263,282,288],"their":[2],"topologies":[3],"are":[4],"critical":[5],"to":[6,64,128,175,206,216,256,285],"nearly":[7],"every":[8],"aspect":[9],"of":[10,48,60,75,90,106,185,210,219,240,247,272,290],"modern":[11],"life,":[12],"with":[13],"social":[14],"networks":[15,21,35],"governing":[16,22],"human":[17],"interactions":[18],"computer":[20],"global":[23],"information-flow.":[24],"Network":[25],"behavior":[26],"is":[27,67,143],"inherently":[28],"structural,":[29],"thus":[31],"modeling":[32,39,56],"data":[33,53,245],"from":[34,37,51,243,279],"benefits":[36],"explicitly":[38,55],"structure.":[40],"This":[41,97],"thesis":[42,98,166,201,231,267],"covers":[43],"methods":[44,262],"for":[45,70,87,94,103,187,236,276],"analysis":[47],"machine":[49,223,277],"learning":[50,234,237,278],"network":[52,244,251,280],"while":[54],"one":[57],"important":[58],"measure":[59],"structure:":[61],"degree.":[62],"Central":[63],"this":[65,165,200,230,266],"work":[66],"a":[68,76,100,156,171,182,233,269],"procedure":[69],"exact":[71,104,141,273],"maximum":[72,108,149],"likelihood":[73,109],"estimation":[74,105,275],"distribution":[77,83,242],"over":[78],"graph":[79,124],"structure,":[80],"where":[81],"the":[82,107,113,118,129,137,148,153,162,177,191,196,208,211,238,241,291],"factorizes":[84],"into":[85],"edge-likelihoods":[86],"each":[88,95],"pair":[89],"nodes":[91,133],"degree-likelihoods":[93],"node.":[96],"provides":[99,181],"novel":[101,183],"method":[102],"edge":[110],"structure":[111],"under":[112],"distribution.":[114],"The":[115,140,260],"algorithm":[116,235],"solves":[117],"optimization":[119],"by":[120,146],"constructing":[121],"an":[122],"augmented":[123,154],"containing,":[125],"in":[126,168,222,265],"addition":[127,215],"original":[130],"nodes,":[131],"auxiliary":[132],"whose":[134],"edges":[135],"encode":[136],"degree":[138,221],"potentials.":[139],"solution":[142],"then":[144],"recoverable":[145],"finding":[147,176],"weight":[150],"b-matching":[151,179,197,212],"on":[152,170,190],"graph,":[155],"well-studied":[157],"combinatorial":[158,163],"optimization.":[159],"To":[160],"solve":[161],"optimization,":[164],"focuses":[167],"particular":[169],"belief":[172,188],"propagation-based":[173],"approach":[174],"optimal":[178],"proof":[184],"convergence":[186],"propagation":[189],"loopy":[192],"graphical":[193],"model":[194],"representing":[195],"objective.":[198],"Additionally,":[199],"describes":[202],"new":[203],"algorithmic":[204],"techniques":[205],"improve":[207],"scalability":[209],"solver.":[213],"In":[214],"various":[217,286],"applications":[218,289],"node":[220,248],"learning,":[224],"including":[225],"classification":[226],"collaborative":[228],"filtering,":[229],"proposes":[232],"parameters":[239],"consisting":[246],"attributes":[249],"connectivity,":[252],"using":[253],"strategies":[254],"similar":[255],"maximum-margin":[257],"structured":[258],"prediction.":[259],"main":[261,292],"results":[264],"represent":[268],"deep":[270],"exploration":[271],"degree-based":[274],"data,":[281],"furthermore":[283],"lead":[284],"extensions":[287],"idea":[293],"described":[294],"within.":[295]},"counts_by_year":[],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2016-06-24T00:00:00"}
