{"id":"https://openalex.org/W3124456076","doi":"https://doi.org/10.3390/e23010123","title":"Variationally Inferred Sampling through a Refined Bound","display_name":"Variationally Inferred Sampling through a Refined Bound","publication_year":2021,"publication_date":"2021-01-19","ids":{"openalex":"https://openalex.org/W3124456076","doi":"https://doi.org/10.3390/e23010123","mag":"3124456076","pmid":"https://pubmed.ncbi.nlm.nih.gov/33477766"},"language":"en","primary_location":{"id":"doi:10.3390/e23010123","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010123","pdf_url":"https://www.mdpi.com/1099-4300/23/1/123/pdf?version=1611035105","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/1/123/pdf?version=1611035105","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027805517","display_name":"V\u00edctor Gallego","orcid":"https://orcid.org/0000-0003-0349-0714"},"institutions":[{"id":"https://openalex.org/I1343558604","display_name":"Statistical and Applied Mathematical Sciences Institute","ror":"https://ror.org/01shctp43","country_code":"US","type":"facility","lineage":["https://openalex.org/I1311060795","https://openalex.org/I1343558604"]},{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]}],"countries":["ES","US"],"is_corresponding":true,"raw_author_name":"V\u00edctor Gallego","raw_affiliation_strings":["Institute of Mathematical Sciences (ICMAT), 28049 Madrid, Spain","Statistical and Applied Mathematical Sciences Institute, Durham, NC 7333, USA"],"raw_orcid":"https://orcid.org/0000-0003-0349-0714","affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences (ICMAT), 28049 Madrid, Spain","institution_ids":["https://openalex.org/I4210157032"]},{"raw_affiliation_string":"Statistical and Applied Mathematical Sciences Institute, Durham, NC 7333, USA","institution_ids":["https://openalex.org/I1343558604"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065634152","display_name":"David R\u0131\u0301os Insua","orcid":"https://orcid.org/0000-0002-5748-9658"},"institutions":[{"id":"https://openalex.org/I148128674","display_name":"University of Shanghai for Science and Technology","ror":"https://ror.org/00ay9v204","country_code":"CN","type":"education","lineage":["https://openalex.org/I148128674"]},{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]}],"countries":["CN","ES"],"is_corresponding":false,"raw_author_name":"David R\u00edos Insua","raw_affiliation_strings":["Institute of Mathematical Sciences (ICMAT), 28049 Madrid, Spain","School of Management, University of Shanghai for Science and Technology, Shanghai 201206, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences (ICMAT), 28049 Madrid, Spain","institution_ids":["https://openalex.org/I4210157032"]},{"raw_affiliation_string":"School of Management, University of Shanghai for Science and Technology, Shanghai 201206, China","institution_ids":["https://openalex.org/I148128674"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027805517"],"corresponding_institution_ids":["https://openalex.org/I1343558604","https://openalex.org/I4210157032"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6996,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.75130363,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":"1","first_page":"123","last_page":"123"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9972000122070312,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9972000122070312,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9936000108718872,"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/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.495025098323822},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.45056265592575073},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4462611675262451},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3835427761077881},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35627299547195435},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.3514617085456848},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.30635032057762146},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1252288520336151}],"concepts":[{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.495025098323822},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45056265592575073},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4462611675262451},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3835427761077881},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35627299547195435},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.3514617085456848},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30635032057762146},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1252288520336151},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/e23010123","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010123","pdf_url":"https://www.mdpi.com/1099-4300/23/1/123/pdf?version=1611035105","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:33477766","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33477766","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:digital.csic.es:10261/261252","is_oa":false,"landing_page_url":"http://hdl.handle.net/10261/261252","pdf_url":null,"source":{"id":"https://openalex.org/S4306400616","display_name":"DIGITAL.CSIC (Spanish National Research Council (CSIC))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I134820265","host_organization_name":"Consejo Superior de Investigaciones Cient\u00edficas","host_organization_lineage":["https://openalex.org/I134820265"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"art\u00edculo"},{"id":"pmh:oai:doaj.org/article:73f0661639154955a23effef7e82a53a","is_oa":true,"landing_page_url":"https://doaj.org/article/73f0661639154955a23effef7e82a53a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 23, Iss 1, p 123 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/1/123/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23010123","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":"Entropy; Volume 23; Issue 1; Pages: 123","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7832329","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7832329","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:www.ucm.es:75595","is_oa":true,"landing_page_url":"https://eprints.ucm.es/id/eprint/75595/1/gallego_variationally_entropy.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400298","display_name":"Library Open Repository (Universidad Complutense Madrid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I121748325","host_organization_name":"Universidad Complutense de Madrid","host_organization_lineage":["https://openalex.org/I121748325"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/e23010123","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010123","pdf_url":"https://www.mdpi.com/1099-4300/23/1/123/pdf?version=1611035105","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1623582559","display_name":null,"funder_award_id":"MTM2017-86875-C3-1-R","funder_id":"https://openalex.org/F4320326262","funder_display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a"},{"id":"https://openalex.org/G2447975439","display_name":null,"funder_award_id":"CEX2019-000904-S","funder_id":"https://openalex.org/F4320326262","funder_display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a"},{"id":"https://openalex.org/G8545601389","display_name":null,"funder_award_id":"PU16-05034","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G8644590155","display_name":null,"funder_award_id":"MS-1638521","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320321048","display_name":"AXA Research Fund","ror":"https://ror.org/02zxqxw53"},{"id":"https://openalex.org/F4320326262","display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a","ror":"https://ror.org/03sv46s19"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3124456076.pdf","grobid_xml":"https://content.openalex.org/works/W3124456076.grobid-xml"},"referenced_works_count":70,"referenced_works":["https://openalex.org/W117969194","https://openalex.org/W299440670","https://openalex.org/W590322889","https://openalex.org/W621546036","https://openalex.org/W777381104","https://openalex.org/W1501586228","https://openalex.org/W1517555081","https://openalex.org/W1524172054","https://openalex.org/W1623643235","https://openalex.org/W1906598733","https://openalex.org/W1997628954","https://openalex.org/W2025720061","https://openalex.org/W2099471712","https://openalex.org/W2112820511","https://openalex.org/W2125838338","https://openalex.org/W2151926297","https://openalex.org/W2167433878","https://openalex.org/W2225156818","https://openalex.org/W2234809627","https://openalex.org/W2238987678","https://openalex.org/W2295803031","https://openalex.org/W2323824333","https://openalex.org/W2478027467","https://openalex.org/W2511837229","https://openalex.org/W2577537660","https://openalex.org/W2594374979","https://openalex.org/W2594830834","https://openalex.org/W2736897279","https://openalex.org/W2739517340","https://openalex.org/W2750384547","https://openalex.org/W2784067649","https://openalex.org/W2785331752","https://openalex.org/W2786540237","https://openalex.org/W2799120050","https://openalex.org/W2803474767","https://openalex.org/W2803981139","https://openalex.org/W2886436016","https://openalex.org/W2889762000","https://openalex.org/W2897613819","https://openalex.org/W2898043227","https://openalex.org/W2899642877","https://openalex.org/W2902858271","https://openalex.org/W2920868047","https://openalex.org/W2944347733","https://openalex.org/W2947433899","https://openalex.org/W2950873402","https://openalex.org/W2950942124","https://openalex.org/W2951004968","https://openalex.org/W2954040150","https://openalex.org/W2962727772","https://openalex.org/W2962915600","https://openalex.org/W2962994101","https://openalex.org/W2970682219","https://openalex.org/W2970810127","https://openalex.org/W2970971581","https://openalex.org/W2979719808","https://openalex.org/W3099467939","https://openalex.org/W3099964132","https://openalex.org/W3101380508","https://openalex.org/W4238209390","https://openalex.org/W4285719527","https://openalex.org/W6610566761","https://openalex.org/W6631656437","https://openalex.org/W6638674303","https://openalex.org/W6638908295","https://openalex.org/W6685480099","https://openalex.org/W6696727771","https://openalex.org/W6736221594","https://openalex.org/W6752474965","https://openalex.org/W6753361586"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"In":[0],"this":[1,30],"work,":[2],"a":[3,19,24,51,82,89,94],"framework":[4,31],"to":[5,50,60],"boost":[6],"the":[7,43],"efficiency":[8],"of":[9,40,46],"Bayesian":[10],"inference":[11],"in":[12],"probabilistic":[13],"models":[14,78],"is":[15,73],"introduced":[16],"by":[17],"embedding":[18],"Markov":[20],"chain":[21],"sampler":[22,47],"within":[23],"variational":[25,33,83,91],"posterior":[26],"approximation.":[27],"We":[28],"call":[29],"\"refined":[32],"approximation\".":[34],"Its":[35,70],"strengths":[36],"are":[37,67],"its":[38],"ease":[39],"implementation":[41],"and":[42,88],"automatic":[44,56],"tuning":[45],"parameters,":[48],"leading":[49],"faster":[52],"mixing":[53],"time":[54],"through":[55],"differentiation.":[57],"Several":[58],"strategies":[59],"approximate":[61],"evidence":[62],"lower":[63],"bound":[64],"(ELBO)":[65],"computation":[66],"also":[68],"introduced.":[69],"efficient":[71],"performance":[72],"showcased":[74],"experimentally":[75],"using":[76],"state-space":[77],"for":[79,85],"time-series":[80],"data,":[81],"encoder":[84],"density":[86],"estimation":[87],"conditional":[90],"autoencoder":[92],"as":[93],"deep":[95],"Bayes":[96],"classifier.":[97]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}