{"id":"https://openalex.org/W3111369083","doi":"https://doi.org/10.3390/a13120329","title":"Hard and Soft EM in Bayesian Network Learning from Incomplete Data","display_name":"Hard and Soft EM in Bayesian Network Learning from Incomplete Data","publication_year":2020,"publication_date":"2020-12-09","ids":{"openalex":"https://openalex.org/W3111369083","doi":"https://doi.org/10.3390/a13120329","mag":"3111369083"},"language":"en","primary_location":{"id":"doi:10.3390/a13120329","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13120329","pdf_url":"https://www.mdpi.com/1999-4893/13/12/329/pdf?version=1607603419","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/13/12/329/pdf?version=1607603419","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060234914","display_name":"Andrea Ruggieri","orcid":"https://orcid.org/0000-0002-2509-271X"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Ruggieri","raw_affiliation_strings":["Department of Informatics, Systems and Communication, Universit\u00e0 degli Studi di Milano-Bicocca, 20126 Milano, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, Systems and Communication, Universit\u00e0 degli Studi di Milano-Bicocca, 20126 Milano, Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086094242","display_name":"Francesco Stranieri","orcid":"https://orcid.org/0000-0002-5366-8499"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Stranieri","raw_affiliation_strings":["Department of Informatics, Systems and Communication, Universit\u00e0 degli Studi di Milano-Bicocca, 20126 Milano, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, Systems and Communication, Universit\u00e0 degli Studi di Milano-Bicocca, 20126 Milano, Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020281960","display_name":"Fabio Stella","orcid":"https://orcid.org/0000-0002-1394-0507"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fabio Stella","raw_affiliation_strings":["Department of Informatics, Systems and Communication, Universit\u00e0 degli Studi di Milano-Bicocca, 20126 Milano, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, Systems and Communication, Universit\u00e0 degli Studi di Milano-Bicocca, 20126 Milano, Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059820079","display_name":"Marco Scutari","orcid":"https://orcid.org/0000-0002-2151-7266"},"institutions":[{"id":"https://openalex.org/I2614128279","display_name":"Dalle Molle Institute for Artificial Intelligence Research","ror":"https://ror.org/013355g38","country_code":"CH","type":"facility","lineage":["https://openalex.org/I15196421","https://openalex.org/I2614128279","https://openalex.org/I57201433"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Marco Scutari","raw_affiliation_strings":["Istituto Dalle Molle di Studi sull\u2019Intelligenza Artificiale (IDSIA), 6962 Viganello, Switzerland","Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA), 6962 Viganello, Switzerland"],"affiliations":[{"raw_affiliation_string":"Istituto Dalle Molle di Studi sull\u2019Intelligenza Artificiale (IDSIA), 6962 Viganello, Switzerland","institution_ids":["https://openalex.org/I2614128279"]},{"raw_affiliation_string":"Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA), 6962 Viganello, Switzerland","institution_ids":["https://openalex.org/I2614128279"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5059820079"],"corresponding_institution_ids":["https://openalex.org/I2614128279"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.6456,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.87609051,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"13","issue":"12","first_page":"329","last_page":"329"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9998999834060669,"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":0.9998999834060669,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9621000289916992,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9379000067710876,"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/bayesian-network","display_name":"Bayesian network","score":0.767516016960144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7361563444137573},{"id":"https://openalex.org/keywords/missing-data","display_name":"Missing data","score":0.6278964281082153},{"id":"https://openalex.org/keywords/imputation","display_name":"Imputation (statistics)","score":0.5453502535820007},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.5085073709487915},{"id":"https://openalex.org/keywords/graphical-model","display_name":"Graphical model","score":0.4920160472393036},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.46526551246643066},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.464490681886673},{"id":"https://openalex.org/keywords/decision-tree","display_name":"Decision tree","score":0.4609670341014862},{"id":"https://openalex.org/keywords/belief-propagation","display_name":"Belief propagation","score":0.4423346519470215},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3506423830986023}],"concepts":[{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.767516016960144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7361563444137573},{"id":"https://openalex.org/C9357733","wikidata":"https://www.wikidata.org/wiki/Q6878417","display_name":"Missing data","level":2,"score":0.6278964281082153},{"id":"https://openalex.org/C58041806","wikidata":"https://www.wikidata.org/wiki/Q1660484","display_name":"Imputation (statistics)","level":3,"score":0.5453502535820007},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5085073709487915},{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.4920160472393036},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.46526551246643066},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.464490681886673},{"id":"https://openalex.org/C84525736","wikidata":"https://www.wikidata.org/wiki/Q831366","display_name":"Decision tree","level":2,"score":0.4609670341014862},{"id":"https://openalex.org/C152948882","wikidata":"https://www.wikidata.org/wiki/Q4060686","display_name":"Belief propagation","level":3,"score":0.4423346519470215},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3506423830986023},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/a13120329","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13120329","pdf_url":"https://www.mdpi.com/1999-4893/13/12/329/pdf?version=1607603419","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2012.05269","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.05269","pdf_url":"https://arxiv.org/pdf/2012.05269","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:boa.unimib.it:10281/302797","is_oa":true,"landing_page_url":"http://hdl.handle.net/10281/302797","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:5eda27895a42401eae6209ed68672656","is_oa":true,"landing_page_url":"https://doaj.org/article/5eda27895a42401eae6209ed68672656","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 13, Iss 12, p 329 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/13/12/329/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a13120329","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 13; Issue 12; Pages: 329","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a13120329","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13120329","pdf_url":"https://www.mdpi.com/1999-4893/13/12/329/pdf?version=1607603419","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3111369083.pdf","grobid_xml":"https://content.openalex.org/works/W3111369083.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W613321770","https://openalex.org/W1511986666","https://openalex.org/W1517993545","https://openalex.org/W1523680690","https://openalex.org/W1536282935","https://openalex.org/W1566045017","https://openalex.org/W1570770495","https://openalex.org/W2038374320","https://openalex.org/W2044758663","https://openalex.org/W2049633694","https://openalex.org/W2074184525","https://openalex.org/W2096863518","https://openalex.org/W2100358124","https://openalex.org/W2127841934","https://openalex.org/W2134843796","https://openalex.org/W2147234027","https://openalex.org/W2149337551","https://openalex.org/W2168175751","https://openalex.org/W2496114304","https://openalex.org/W2498094064","https://openalex.org/W2565618151","https://openalex.org/W2757933965","https://openalex.org/W2955443275","https://openalex.org/W2964071773","https://openalex.org/W2999231652","https://openalex.org/W4232344051","https://openalex.org/W6632151551","https://openalex.org/W6633761756","https://openalex.org/W6659852763","https://openalex.org/W6681979088"],"related_works":["https://openalex.org/W2181530120","https://openalex.org/W4211215373","https://openalex.org/W2024529227","https://openalex.org/W1574575415","https://openalex.org/W3144172081","https://openalex.org/W3179858851","https://openalex.org/W3028371478","https://openalex.org/W2081476516","https://openalex.org/W2581984549","https://openalex.org/W3123177881"],"abstract_inverted_index":{"Incomplete":[0],"data":[1,36,91,142],"are":[2,18],"a":[3,137,176],"common":[4],"feature":[5],"in":[6,21,159,183],"many":[7],"domains,":[8],"from":[9,34,70],"clinical":[10],"trials":[11],"to":[12,94,152,174,180,190],"industrial":[13],"applications.":[14],"Bayesian":[15],"networks":[16],"(BNs)":[17],"often":[19,88],"used":[20],"these":[22],"domains":[23],"because":[24],"of":[25,67,83,99,106,122,126,132,166],"their":[26,191],"graphical":[27],"and":[28,85,108,143],"causal":[29],"interpretations.":[30],"BN":[31,69],"parameter":[32,84],"learning":[33,87],"incomplete":[35],"is":[37,119,150],"usually":[38],"implemented":[39],"with":[40],"the":[41,47,57,64,68,116,120,130,133,157,164,167,185],"Expectation-Maximisation":[42,59],"algorithm":[43,60,187],"(EM),":[44],"which":[45],"computes":[46],"relevant":[48],"sufficient":[49,72,96],"statistics":[50,73,97],"(\u201csoft":[51],"EM\u201d)":[52,93],"using":[53,74,100,123,140],"belief":[54,101,127],"propagation.":[55],"Similarly,":[56],"Structural":[58],"(Structural":[61],"EM)":[62],"learns":[63],"network":[65],"structure":[66,86],"those":[71],"algorithms":[75],"designed":[76],"for":[77,103],"complete":[78],"data.":[79,168],"However,":[80],"practical":[81],"implementations":[82],"impute":[89],"missing":[90],"(\u201chard":[92],"compute":[95],"instead":[98,125],"propagation,":[102],"both":[104],"ease":[105],"implementation":[107],"computational":[109],"speed.":[110],"In":[111],"this":[112,172],"paper,":[113],"we":[114,146],"investigate":[115],"question:":[117],"what":[118],"impact":[121],"imputation":[124],"propagation":[128],"on":[129,163],"quality":[131],"resulting":[134],"BNs?":[135],"From":[136],"simulation":[138],"study":[139],"synthetic":[141],"reference":[144],"BNs,":[145],"find":[147],"that":[148],"it":[149],"possible":[151],"recommend":[153],"one":[154],"approach":[155],"over":[156],"other":[158],"several":[160],"scenarios":[161],"based":[162],"characteristics":[165],"We":[169],"then":[170],"use":[171],"information":[173],"build":[175],"simple":[177],"decision":[178],"tree":[179],"guide":[181],"practitioners":[182],"choosing":[184],"EM":[186],"best":[188],"suited":[189],"problem.":[192]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
