{"id":"https://openalex.org/W2997400537","doi":"https://doi.org/10.5555/2789272.2912081","title":"Counting and exploring sizes of Markov equivalence classes of directed acyclic graphs","display_name":"Counting and exploring sizes of Markov equivalence classes of directed acyclic graphs","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2997400537","doi":"https://doi.org/10.5555/2789272.2912081","mag":"2997400537"},"language":"en","primary_location":{"id":"mag:2997400537","is_oa":false,"landing_page_url":"https://dl.acm.org/doi/10.5555/2789272.2912081","pdf_url":null,"source":{"id":"https://openalex.org/S118988714","display_name":"Journal of Machine Learning Research","issn_l":"1532-4435","issn":["1532-4435","1533-7928"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Journal of Machine Learning Research","raw_type":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/A5002385542","display_name":"HeYangbo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"HeYangbo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077719311","display_name":"JiaJinzhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"JiaJinzhu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5053679514","display_name":"Yubin Yubin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yubin Yubin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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":0.26133694,"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":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.980400025844574,"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":0.980400025844574,"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/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.8045079708099365},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6272954940795898},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6035236716270447},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5588003396987915},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5044604539871216},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4653749167919159},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.46336740255355835},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3349403142929077},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18864065408706665}],"concepts":[{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.8045079708099365},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6272954940795898},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6035236716270447},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5588003396987915},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5044604539871216},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4653749167919159},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.46336740255355835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3349403142929077},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18864065408706665}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2997400537","is_oa":false,"landing_page_url":"https://dl.acm.org/doi/10.5555/2789272.2912081","pdf_url":null,"source":{"id":"https://openalex.org/S118988714","display_name":"Journal of Machine Learning Research","issn_l":"1532-4435","issn":["1532-4435","1533-7928"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Journal of Machine Learning Research","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2280205447","https://openalex.org/W3003611953","https://openalex.org/W2963487771","https://openalex.org/W2949461610","https://openalex.org/W2038769064","https://openalex.org/W2556178492","https://openalex.org/W2964304674","https://openalex.org/W2963293157","https://openalex.org/W1596818943","https://openalex.org/W2055626750","https://openalex.org/W2182129176","https://openalex.org/W2111061246","https://openalex.org/W824890361","https://openalex.org/W79495945","https://openalex.org/W2109587480","https://openalex.org/W2918208206","https://openalex.org/W2158361602","https://openalex.org/W1533258541","https://openalex.org/W2023711046","https://openalex.org/W1824511011"],"abstract_inverted_index":{"When":[0],"learning":[1],"a":[2,22],"directed":[3],"acyclic":[4],"graph":[5],"(DAG)":[6],"model":[7],"via":[8],"observational":[9],"data,":[10],"one":[11],"generally":[12],"cannot":[13],"identify":[14],"the":[15],"underlying":[16],"DAG,":[17],"but":[18],"can":[19],"potentially":[20],"obtain":[21],"Markov":[23],"equivalence":[24],"class.":[25],"The":[26],"size":[27],"(the":[28],"num...":[29]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}