{"id":"https://openalex.org/W2158132003","doi":"https://doi.org/10.48550/arxiv.1409.3836","title":"Hardness of parameter estimation in graphical models","display_name":"Hardness of parameter estimation in graphical models","publication_year":2014,"publication_date":"2014-09-12","ids":{"openalex":"https://openalex.org/W2158132003","doi":"https://doi.org/10.48550/arxiv.1409.3836","mag":"2158132003"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1409.3836","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1409.3836","pdf_url":"https://arxiv.org/pdf/1409.3836","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1409.3836","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060812074","display_name":"Guy Bresler","orcid":"https://orcid.org/0009-0007-6716-8827","observed_orcids":["https://orcid.org/0009-0007-6716-8827","https://orcid.org/0000-0003-1303-582X"]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bresler, Guy","raw_affiliation_strings":["Laboratory for Information and Decision Systems Department of EECS and Sloan School of Management","Laboratory for Information and Decision Systems, Department of EECS, Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems Department of EECS and Sloan School of Management","institution_ids":[]},{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Department of EECS, Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031648070","display_name":"David Gamarnik","orcid":"https://orcid.org/0000-0001-8898-8778","observed_orcids":["https://orcid.org/0000-0001-8898-8778"]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gamarnik, David","raw_affiliation_strings":["Massachusetts Institute of Technology","Laboratory for Information and Decision Systems, Sloan School of Management, Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Sloan School of Management, Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029499294","display_name":"Devavrat Shah B","orcid":"https://orcid.org/0000-0003-0737-3259","observed_orcids":["https://orcid.org/0000-0003-0737-3259"]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shah, Devavrat","raw_affiliation_strings":["Laboratory for Information and Decision Systems Department of EECS and Sloan School of Management","Laboratory for Information and Decision Systems, Department of EECS, Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems Department of EECS and Sloan School of Management","institution_ids":[]},{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Department of EECS, Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":null,"first_page":"1062","last_page":"1070"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9657999873161316,"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":0.9657999873161316,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.013799999840557575,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.01119999960064888,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parameter-estimation","display_name":"parameter estimation","score":0.7749999761581421},{"id":"https://openalex.org/keywords/undirected-graphical-models","display_name":"undirected graphical models","score":0.9430000185966492},{"id":"https://openalex.org/keywords/markov-random-fields","display_name":"Markov random fields","score":0.9980000257492065},{"id":"https://openalex.org/keywords/canonical-parameters","display_name":"canonical parameters","score":0.8479999899864197},{"id":"https://openalex.org/keywords/intractability","display_name":"computational intractability","score":0.8220000267028809},{"id":"https://openalex.org/keywords/hardness-of-approximation","display_name":"hardness of approximation","score":0.7049999833106995},{"id":"https://openalex.org/keywords/partition-function","display_name":"partition function","score":0.5009999871253967},{"id":"https://openalex.org/keywords/hard-core-model","display_name":"hard-core model","score":0.9980000257492065},{"id":"https://openalex.org/keywords/polynomial-time-reduction","display_name":"polynomial-time reduction","score":0.6230000257492065},{"id":"https://openalex.org/keywords/exponential-family","display_name":"exponential family","score":0.47600001096725464}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7472586035728455},{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.6729578971862793},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6400223970413208},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6250427961349487},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.6047691702842712},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49279168248176575},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.451994925737381},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41442710161209106},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39176085591316223},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37369459867477417},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3181881904602051},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:arXiv.org:1409.3836","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1409.3836","pdf_url":"https://arxiv.org/pdf/1409.3836","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2158132003","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1409.3836v2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.740.1408","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.740.1408","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1409.3836.pdf","raw_type":"text"},{"id":"pmh:oai:dspace.mit.edu:1721.1/101045","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/1721.1/101045","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MIT web domain","raw_type":"http://purl.org/eprint/type/ConferencePaper"},{"id":"doi:10.48550/arxiv.1409.3836","doi":"https://doi.org/10.48550/arxiv.1409.3836","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1409.3836","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"Preprint"},{"id":"mag:2964313593","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1409.3836","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1409.3836","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1409.3836","pdf_url":"https://arxiv.org/pdf/1409.3836","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2883152915","display_name":null,"funder_award_id":"W911NF-11-1-0036","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G5808922519","display_name":"Local Algorithms for Random Networks: Power, Limitations and Applications","funder_award_id":"1335155","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6444210580","display_name":"NeTS: Medium: Cortex: Rateless Wireless Networking Using Spinal Codes","funder_award_id":"1161964","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G862988727","display_name":null,"funder_award_id":"W911NF-11","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W2004724832","https://openalex.org/W2024710200","https://openalex.org/W2039763834","https://openalex.org/W2068524660","https://openalex.org/W2073608764","https://openalex.org/W2084392902","https://openalex.org/W2086333739","https://openalex.org/W2120078542","https://openalex.org/W2120340025","https://openalex.org/W2121562066","https://openalex.org/W2123589260","https://openalex.org/W2158907148","https://openalex.org/W2165356592","https://openalex.org/W2798766386","https://openalex.org/W2953045501","https://openalex.org/W3111890340","https://openalex.org/W3141595720"],"related_works":["https://openalex.org/W2964313593","https://openalex.org/W2900260669","https://openalex.org/W1895639643","https://openalex.org/W3104704650","https://openalex.org/W3181255818","https://openalex.org/W2963055343","https://openalex.org/W2962894425","https://openalex.org/W2254026354","https://openalex.org/W838635703","https://openalex.org/W2294296233","https://openalex.org/W2149263910","https://openalex.org/W3099147999","https://openalex.org/W2953107765","https://openalex.org/W2616292232","https://openalex.org/W2908456597","https://openalex.org/W3164935232","https://openalex.org/W2950298468","https://openalex.org/W1949099970","https://openalex.org/W1964669306","https://openalex.org/W3006926186"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,6,18,29,36,40,54,76,87,97,116,137,141,157,172,186],"problem":[3,41],"of":[4,48,57,79,99,140,180],"learning":[5,149],"canonical":[7,30,77],"parameters":[8,31,78,89],"specifying":[9],"an":[10,162,168],"undirected":[11],"graphical":[12,22,84],"model":[13,85],"(Markov":[14],"random":[15],"field)":[16],"from":[17,86,135],"mean":[19,37,88],"parameters.":[20,151],"For":[21],"models":[23],"representing":[24],"a":[25,80,94,107,131],"minimal":[26],"exponential":[27],"family,":[28],"are":[32],"uniquely":[33],"determined":[34],"by":[35,93,118,185],"parameters,":[38],"so":[39],"is":[42,51,68],"feasible":[43],"in":[44,69,90,96],"principle.":[45],"The":[46],"goal":[47],"this":[49,58],"paper":[50],"to":[52,112,145,148],"investigate":[53],"computational":[55],"feasibility":[56],"statistical":[59],"task.":[60],"Our":[61,128,152],"main":[62],"result":[63,108],"shows":[64],"that":[65,156,174],"parameter":[66],"estimation":[67],"general":[70],"intractable:":[71],"no":[72,124],"algorithm":[73],"can":[74],"learn":[75],"generic":[81],"pair-wise":[82],"binary":[83],"time":[91,133],"bounded":[92],"polynomial":[95,132],"number":[98],"variables":[100],"(unless":[101],"RP":[102],"=":[103],"NP).":[104],"Indeed,":[105],"such":[106],"has":[109,161],"been":[110],"believed":[111],"be":[113,146],"true":[114],"(see":[115],"monograph":[117],"Wainwright":[119],"and":[120,189],"Jordan":[121],"(2008))":[122],"but":[123],"proof":[125,129],"was":[126],"known.":[127],"gives":[130],"reduction":[134,153],"approximating":[136],"partition":[138],"function":[139],"hard-core":[142],"model,":[143],"known":[144],"hard,":[147],"approximate":[150],"entails":[154],"showing":[155],"marginal":[158],"polytope":[159,173],"boundary":[160],"inherent":[163],"repulsive":[164],"property,":[165],"which":[166],"validates":[167],"optimization":[169],"procedure":[170],"over":[171],"does":[175],"not":[176],"use":[177],"any":[178],"knowledge":[179],"its":[181],"structure":[182],"(as":[183],"required":[184],"ellipsoid":[187],"method":[188],"others).":[190]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-10-17T09:40:24.721904","created_date":"2025-10-10T00:00:00"}