{"id":"https://openalex.org/W4416016831","doi":"https://doi.org/10.1145/3746252.3761065","title":"Tight Bounds for Jensen's Gap with Applications to Variational Inference","display_name":"Tight Bounds for Jensen's Gap with Applications to Variational Inference","publication_year":2025,"publication_date":"2025-11-07","ids":{"openalex":"https://openalex.org/W4416016831","doi":"https://doi.org/10.1145/3746252.3761065"},"language":"en","primary_location":{"id":"doi:10.1145/3746252.3761065","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3746252.3761065","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 34th ACM International Conference on Information and Knowledge Management","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1145/3746252.3761065","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090307584","display_name":"M. Mazur","orcid":"https://orcid.org/0000-0002-3440-8173"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Marcin Mazur","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0002-3440-8173","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107673143","display_name":"Tadeusz Dziarmaga","orcid":"https://orcid.org/0009-0001-8911-0630"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Tadeusz Dziarmaga","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0009-0001-8911-0630","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089800694","display_name":"Piotr Ko\u015bcielniak","orcid":"https://orcid.org/0000-0003-2389-0643"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Piotr Ko\u015bcielniak","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0003-2389-0643","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007063171","display_name":"\u0141ukasz Struski","orcid":"https://orcid.org/0000-0003-4006-356X"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"\u0141ukasz Struski","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0003-4006-356X","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5090307584"],"corresponding_institution_ids":["https://openalex.org/I126596746"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1663484,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"2074","last_page":"2083"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.3138999938964844,"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":0.3138999938964844,"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":0.11490000039339066,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.10840000212192535,"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/probabilistic-logic","display_name":"Probabilistic logic","score":0.6707000136375427},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6234999895095825},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5478000044822693},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5460000038146973},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5414000153541565},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5370000004768372},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5048999786376953},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.44449999928474426}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6707000136375427},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6234999895095825},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5478000044822693},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5460000038146973},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5414000153541565},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5370000004768372},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5073999762535095},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5048999786376953},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4458000063896179},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.44449999928474426},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41179999709129333},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3878999948501587},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3799999952316284},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3783000111579895},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3458000123500824},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.33219999074935913},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.29910001158714294},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2768999934196472},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27000001072883606},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.2574999928474426}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3746252.3761065","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3746252.3761065","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 34th ACM International Conference on Information and Knowledge Management","raw_type":"proceedings-article"},{"id":"pmh:oai:ruj.uj.edu.pl:item/565522","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/handle/item/565522","pdf_url":"http://ruj.uj.edu.pl/bitstreams/628307b2-6a22-4b3d-94a0-0b36e4abcce3/download","source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"doi:10.1145/3746252.3761065","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3746252.3761065","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 34th ACM International Conference on Information and Knowledge Management","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322650","display_name":"Narodowym Centrum Nauki","ror":"https://ror.org/03ha2q922"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1691104707","https://openalex.org/W1834627138","https://openalex.org/W2029029543","https://openalex.org/W2053513467","https://openalex.org/W2060783893","https://openalex.org/W2062484790","https://openalex.org/W2078261139","https://openalex.org/W2112796928","https://openalex.org/W2128606487","https://openalex.org/W2516860936","https://openalex.org/W2739485194","https://openalex.org/W2787931981","https://openalex.org/W3211760805"],"related_works":[],"abstract_inverted_index":{"Since":[0],"its":[1,18],"original":[2],"formulation,":[3],"Jensen's":[4,27,83,127],"inequality":[5],"has":[6,76],"played":[7],"a":[8,36,131],"fundamental":[9],"role":[10],"across":[11],"mathematics,":[12],"statistics,":[13],"and":[14,39,85,89,99,140,149,156],"machine":[15],"learning,":[16],"with":[17,144],"probabilistic":[19,181],"version":[20],"highlighting":[21],"the":[22,25,30,33,40,43,49,52,66,80,96,107,138,141,160,171],"nonnegativity":[23],"of":[24,35,82,109,134,162],"so-called":[26],"gap,":[28],"i.e.,":[29],"difference":[31],"between":[32],"expectation":[34],"convex":[37],"function":[38,41,53,98,139],"at":[42],"expectation.":[44],"Of":[45],"particular":[46],"importance":[47],"is":[48,54,70],"case":[50],"when":[51],"logarithmic,":[55],"as":[56,106],"this":[57,119],"setting":[58],"underpins":[59],"many":[60],"applications":[61],"in":[62,111,180],"variational":[63,68,115],"inference,":[64],"where":[65],"term":[67],"gap":[69,84,128],"often":[71],"used":[72],"interchangeably.":[73],"Recent":[74],"research":[75],"focused":[77],"on":[78,95,136],"estimating":[79],"size":[81],"establishing":[86],"tight":[87],"lower":[88],"upper":[90],"bounds":[91,125,169],"under":[92],"various":[93],"assumptions":[94,135],"underlying":[97],"distribution,":[100],"driven":[101],"by":[102],"practical":[103],"challenges":[104],"such":[105],"intractability":[108],"log-likelihood":[110],"graphical":[112],"models":[113],"like":[114],"autoencoders":[116],"(VAEs).":[117],"In":[118],"paper,":[120],"we":[121,166],"propose":[122],"new,":[123],"general":[124],"for":[126,159],"that":[129],"accommodate":[130],"broad":[132],"range":[133],"both":[137,154],"random":[142],"variable,":[143],"special":[145],"attention":[146],"to":[147,170],"exponential":[148],"logarithmic":[150],"cases.":[151],"We":[152],"provide":[153],"analytical":[155],"empirical":[157],"evidence":[158],"performance":[161,179],"our":[163,168],"method.":[164],"Furthermore,":[165],"relate":[167],"PAC-Bayes":[172],"framework,":[173],"providing":[174],"new":[175],"insights":[176],"into":[177],"generalization":[178],"models.":[182]},"counts_by_year":[],"updated_date":"2026-05-02T08:42:23.175194","created_date":"2025-11-08T00:00:00"}