{"id":"https://openalex.org/W4303183149","doi":"https://doi.org/10.1007/s00180-022-01276-7","title":"Tempered expectation-maximization algorithm for the estimation of discrete latent variable models","display_name":"Tempered expectation-maximization algorithm for the estimation of discrete latent variable models","publication_year":2022,"publication_date":"2022-10-07","ids":{"openalex":"https://openalex.org/W4303183149","doi":"https://doi.org/10.1007/s00180-022-01276-7"},"language":"en","primary_location":{"id":"doi:10.1007/s00180-022-01276-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-022-01276-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-022-01276-7.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00180-022-01276-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001199768","display_name":"Luca Brusa","orcid":"https://orcid.org/0000-0002-8156-470X"},"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":true,"raw_author_name":"Luca Brusa","raw_affiliation_strings":["Department of Economics, Management and Statistics, University of Milano-Bicocca, Milan, Italy"],"raw_orcid":"https://orcid.org/0000-0002-8156-470X","affiliations":[{"raw_affiliation_string":"Department of Economics, Management and Statistics, University of Milano-Bicocca, Milan, Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054448743","display_name":"Francesco Bartolucci","orcid":"https://orcid.org/0000-0001-7057-1421"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Bartolucci","raw_affiliation_strings":["Department of Economics, University of Perugia, Perugia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics, University of Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021943787","display_name":"Fulvia Pennoni","orcid":"https://orcid.org/0000-0002-6331-7211"},"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":"Fulvia Pennoni","raw_affiliation_strings":["Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Milan, Italy","institution_ids":["https://openalex.org/I66752286"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001199768"],"corresponding_institution_ids":["https://openalex.org/I66752286"],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2490,"currency":"EUR","value_usd":3090},"fwci":1.9614,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.87481691,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"38","issue":"3","first_page":"1391","last_page":"1424"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9990000128746033,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9987000226974487,"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":0.9969000220298767,"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/expectation\u2013maximization-algorithm","display_name":"Expectation\u2013maximization algorithm","score":0.7969411015510559},{"id":"https://openalex.org/keywords/latent-variable","display_name":"Latent variable","score":0.6419540643692017},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6114401817321777},{"id":"https://openalex.org/keywords/likelihood-function","display_name":"Likelihood function","score":0.5427707433700562},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5259297490119934},{"id":"https://openalex.org/keywords/latent-class-model","display_name":"Latent class model","score":0.5257664322853088},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.4981968402862549},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4918229579925537},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4898831248283386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4781257212162018},{"id":"https://openalex.org/keywords/latent-variable-model","display_name":"Latent variable model","score":0.4734235107898712},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4697689712047577},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.4340376853942871},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.367236852645874},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.35488206148147583},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23993059992790222}],"concepts":[{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.7969411015510559},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.6419540643692017},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6114401817321777},{"id":"https://openalex.org/C89106044","wikidata":"https://www.wikidata.org/wiki/Q45284","display_name":"Likelihood function","level":3,"score":0.5427707433700562},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5259297490119934},{"id":"https://openalex.org/C70727504","wikidata":"https://www.wikidata.org/wiki/Q1806878","display_name":"Latent class model","level":2,"score":0.5257664322853088},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.4981968402862549},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4918229579925537},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4898831248283386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4781257212162018},{"id":"https://openalex.org/C65965080","wikidata":"https://www.wikidata.org/wiki/Q1806885","display_name":"Latent variable model","level":3,"score":0.4734235107898712},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4697689712047577},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.4340376853942871},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.367236852645874},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.35488206148147583},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23993059992790222},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00180-022-01276-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-022-01276-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-022-01276-7.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:compst:v:38:y:2023:i:3:d:10.1007_s00180-022-01276-7","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00180-022-01276-7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:boa.unimib.it:10281/393748","is_oa":true,"landing_page_url":"http://hdl.handle.net/10281/393748","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"}],"best_oa_location":{"id":"doi:10.1007/s00180-022-01276-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-022-01276-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-022-01276-7.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321610","display_name":"Universit\u00e0 degli Studi di Milano-Bicocca","ror":"https://ror.org/01ynf4891"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4303183149.pdf","grobid_xml":"https://content.openalex.org/works/W4303183149.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W129305155","https://openalex.org/W1882651929","https://openalex.org/W2007463795","https://openalex.org/W2024060531","https://openalex.org/W2043432627","https://openalex.org/W2048899282","https://openalex.org/W2049633694","https://openalex.org/W2056760934","https://openalex.org/W2062828949","https://openalex.org/W2071496798","https://openalex.org/W2086699924","https://openalex.org/W2100923606","https://openalex.org/W2104170278","https://openalex.org/W2115881827","https://openalex.org/W2124369546","https://openalex.org/W2125252492","https://openalex.org/W2133403695","https://openalex.org/W2138309709","https://openalex.org/W2149230623","https://openalex.org/W2157326321","https://openalex.org/W2162896357","https://openalex.org/W2166281097","https://openalex.org/W2168175751","https://openalex.org/W2168303626","https://openalex.org/W2170171286","https://openalex.org/W2257678991","https://openalex.org/W2270140793","https://openalex.org/W2479531384","https://openalex.org/W2498094064","https://openalex.org/W2554987453","https://openalex.org/W2582743722","https://openalex.org/W2766234915","https://openalex.org/W2964036097","https://openalex.org/W2977466517","https://openalex.org/W3012810580","https://openalex.org/W3124427131"],"related_works":["https://openalex.org/W4230230730","https://openalex.org/W1501016332","https://openalex.org/W4237379778","https://openalex.org/W1535265092","https://openalex.org/W4381250654","https://openalex.org/W2103023456","https://openalex.org/W1565287552","https://openalex.org/W2363394205","https://openalex.org/W3109783536","https://openalex.org/W1471855"],"abstract_inverted_index":{"Abstract":[0],"Maximum":[1],"likelihood":[2],"estimation":[3,33],"of":[4,26,63,105,108,120],"discrete":[5,109],"latent":[6,67],"variable":[7],"(DLV)":[8],"models":[9],"is":[10,21,149],"usually":[11],"performed":[12],"by":[13,81],"the":[14,24,27,32,44,55,74,77,90,94,98,103,106,123,129,132,140,144,153],"expectation-maximization":[15],"(EM)":[16],"algorithm.":[17],"A":[18],"well-known":[19],"drawback":[20],"related":[22],"to":[23,37,43,53,92,117,142],"multimodality":[25],"log-likelihood":[28],"function":[29],"so":[30],"that":[31,128],"algorithm":[34,52,80],"can":[35],"converge":[36],"a":[38,49],"local":[39],"maximum,":[40],"not":[41],"corresponding":[42],"global":[45,95,145],"one.":[46],"We":[47,72,101],"propose":[48],"tempered":[50],"EM":[51,79,134],"explore":[54],"parameter":[56],"space":[57],"adequately":[58],"for":[59],"two":[60],"main":[61],"classes":[62],"DLV":[64],"models,":[65],"namely":[66],"class":[68],"and":[69,97,110,113,136],"hidden":[70],"Markov.":[71],"compare":[73],"proposal":[75,130],"with":[76],"standard":[78,133],"an":[82],"extensive":[83],"Monte":[84],"Carlo":[85],"simulation":[86],"study,":[87],"evaluating":[88],"both":[89],"ability":[91],"reach":[93,143],"maximum":[96],"computational":[99],"time.":[100,156],"show":[102],"results":[104,124],"analysis":[107],"continuous":[111],"cross-sectional":[112],"longitudinal":[114],"data":[115],"referring":[116],"some":[118],"applications":[119],"interest.":[121],"All":[122],"provide":[125],"supporting":[126],"evidence":[127],"outperforms":[131],"algorithm,":[135],"it":[137],"significantly":[138],"improves":[139],"chance":[141],"maximum.":[146],"The":[147],"advantage":[148],"relevant":[150],"even":[151],"considering":[152],"overall":[154],"computing":[155]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
