{"id":"https://openalex.org/W7140286115","doi":"https://doi.org/10.48550/arxiv.2603.22959","title":"Stepwise Variational Inference with Vine Copulas","display_name":"Stepwise Variational Inference with Vine Copulas","publication_year":2026,"publication_date":"2026-03-24","ids":{"openalex":"https://openalex.org/W7140286115","doi":"https://doi.org/10.48550/arxiv.2603.22959"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.22959","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22959","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.22959","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120038101","display_name":"Elisabeth Griesbauer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Griesbauer, Elisabeth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089323377","display_name":"Leiv R\u00f8nneberg","orcid":"https://orcid.org/0000-0003-4836-4164"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R\u00f8nneberg, Leiv","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130579301","display_name":"Arnoldo Frigessi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Frigessi, Arnoldo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020151207","display_name":"Claudia Czado","orcid":"https://orcid.org/0000-0002-6329-5438"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Czado, Claudia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011273156","display_name":"Ingrid Hob\u00e6k Haff","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haff, Ingrid Hob\u00e6k","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.34619998931884766,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.34619998931884766,"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":0.16359999775886536,"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":0.14270000159740448,"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/vine-copula","display_name":"Vine copula","score":0.9221000075340271},{"id":"https://openalex.org/keywords/copula","display_name":"Copula (linguistics)","score":0.6313999891281128},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5681999921798706},{"id":"https://openalex.org/keywords/vine","display_name":"Vine","score":0.5346999764442444},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4846999943256378},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.45660001039505005}],"concepts":[{"id":"https://openalex.org/C2779676228","wikidata":"https://www.wikidata.org/wiki/Q25303905","display_name":"Vine copula","level":3,"score":0.9221000075340271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.732200026512146},{"id":"https://openalex.org/C17618745","wikidata":"https://www.wikidata.org/wiki/Q207509","display_name":"Copula (linguistics)","level":2,"score":0.6313999891281128},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5681999921798706},{"id":"https://openalex.org/C2781214258","wikidata":"https://www.wikidata.org/wiki/Q917284","display_name":"Vine","level":2,"score":0.5346999764442444},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4846999943256378},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.45660001039505005},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38769999146461487},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.36169999837875366},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3458000123500824},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3425000011920929},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.34060001373291016},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25189998745918274}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.22959","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22959","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.22959","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22959","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,52],"propose":[1,53],"stepwise":[2,20,63],"variational":[3,25,125],"inference":[4],"(VI)":[5],"with":[6,17,47,157],"vine":[7,15,57,70,88,114],"copulas:":[8],"a":[9,18,31,62,120],"universal":[10],"VI":[11,139],"procedure":[12,22],"that":[13,75],"combines":[14],"copulas":[16,28],"novel":[19],"estimation":[21],"of":[23,30,34,50,123],"the":[24,56,69,76,83,87,92,100,113,116,124],"parameters.":[26],"Vine":[27],"consist":[29],"nested":[32],"sequence":[33],"trees":[35,111],"built":[36],"from":[37],"copulas,":[38],"where":[39],"more":[40],"complex":[41],"latent":[42,143],"dependence":[43],"can":[44],"be":[45],"modeled":[46],"increasing":[48],"number":[49],"trees.":[51],"to":[54,112,118],"estimate":[55],"copula":[58,89],"approximate":[59],"posterior":[60],"in":[61,86,148],"fashion,":[64],"tree":[65,67],"by":[66],"along":[68],"structure.":[71],"Further,":[72],"we":[73],"show":[74],"usual":[77],"backward":[78],"Kullback-Leibler":[79],"divergence":[80],"cannot":[81],"recover":[82],"correct":[84],"parameters":[85],"model,":[90],"thus":[91],"evidence":[93],"lower":[94],"bound":[95],"is":[96,155],"defined":[97],"based":[98],"on":[99],"R\u00e9nyi":[101],"divergence.":[102],"Finally,":[103],"an":[104],"intuitive":[105],"stopping":[106],"criterion":[107],"for":[108,129],"adding":[109],"further":[110],"eliminates":[115],"need":[117],"pre-define":[119],"complexity":[121],"parameter":[122],"distribution,":[126],"as":[127],"required":[128],"most":[130],"other":[131],"approaches.":[132],"Thus,":[133],"our":[134,153],"method":[135,154],"interpolates":[136],"between":[137],"mean-field":[138],"(MFVI)":[140],"and":[141],"full":[142],"dependence.":[144],"In":[145],"many":[146],"applications,":[147],"particular":[149],"sparse":[150],"Gaussian":[151],"processes,":[152],"parsimonious":[156],"parameters,":[158],"while":[159],"outperforming":[160],"MFVI.":[161]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-26T00:00:00"}