{"id":"https://openalex.org/W7140077375","doi":"https://doi.org/10.48550/arxiv.2603.19792","title":"Scalable Learning of Multivariate Distributions via Coresets","display_name":"Scalable Learning of Multivariate Distributions via Coresets","publication_year":2026,"publication_date":"2026-03-20","ids":{"openalex":"https://openalex.org/W7140077375","doi":"https://doi.org/10.48550/arxiv.2603.19792"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.19792","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19792","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.19792","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077435054","display_name":"Zeyu Ding","orcid":"https://orcid.org/0000-0003-1132-7079"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ding, Zeyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063815245","display_name":"Katja Ickstadt","orcid":"https://orcid.org/0000-0001-5157-2496"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ickstadt, Katja","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120774774","display_name":"Nadja Klein","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Klein, Nadja","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023613530","display_name":"Alexander Munteanu","orcid":"https://orcid.org/0000-0001-6549-3270"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Munteanu, Alexander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130360870","display_name":"Simon Omlor","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Omlor, Simon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.2930999994277954,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.2930999994277954,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.20399999618530273,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.1160999983549118,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/scalability","display_name":"Scalability","score":0.6245999932289124},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5105000138282776},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.48570001125335693},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4593000113964081},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.44920000433921814},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43950000405311584},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4269999861717224},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4219000041484833},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.4138000011444092}],"concepts":[{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6245999932289124},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6003000140190125},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5105000138282776},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.48570001125335693},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4593000113964081},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.44920000433921814},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43950000405311584},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4269999861717224},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4219000041484833},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.4138000011444092},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4108999967575073},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.4002000093460083},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3822999894618988},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37059998512268066},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.3440000116825104},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3398999869823456},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3260999917984009},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3230000138282776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32019999623298645},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C56435381","wikidata":"https://www.wikidata.org/wiki/Q1196371","display_name":"Geometric transformation","level":3,"score":0.2815999984741211},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.28040000796318054},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.19792","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19792","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.19792","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19792","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"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":{"Efficient":[0],"and":[1,8,20,55,97,126,161,181,197],"scalable":[2],"non-parametric":[3],"or":[4],"semi-parametric":[5,70,115],"regression":[6],"analysis":[7],"density":[9],"estimation":[10],"are":[11,26,65,129],"of":[12,18,61,95,154,169,192],"crucial":[13],"importance":[14,80],"to":[15,31,51,104],"the":[16,59,66,88,151,186,195],"fields":[17],"statistics":[19,196],"machine":[21,198],"learning.":[22],"However,":[23],"available":[24],"methods":[25],"limited":[27],"in":[28,121,164],"their":[29,53],"ability":[30],"handle":[32],"large-scale":[33],"data.":[34,156,170],"We":[35],"address":[36,136],"this":[37],"issue":[38],"by":[39],"developing":[40],"a":[41,146,189],"novel":[42],"coreset":[43],"construction":[44],"for":[45,69,188],"multivariate":[46],"conditional":[47],"transformation":[48],"models":[49],"(MCTMs)":[50],"enhance":[52],"scalability":[54],"training":[56],"efficiency.":[57],"To":[58,135],"best":[60],"our":[62,114],"knowledge,":[63],"these":[64],"first":[67],"coresets":[68,109],"distributional":[71],"models.":[72],"Our":[73],"approach":[74,116],"yields":[75],"substantial":[76],"data":[77],"reduction":[78],"via":[79],"sampling.":[81],"It":[82],"ensures":[83,158],"with":[84,140],"high":[85],"probability":[86],"that":[87],"log-likelihood":[89],"remains":[90],"within":[91,194],"multiplicative":[92],"error":[93],"bounds":[94],"$(1\\pm\\varepsilon)$":[96],"thereby":[98],"maintains":[99],"statistical":[100],"model":[101],"accuracy.":[102],"Compared":[103],"conventional":[105],"full-parametric":[106],"models,":[107],"where":[108,123],"have":[110],"been":[111],"incorporated":[112],"before,":[113],"exhibits":[117],"enhanced":[118],"adaptability,":[119],"particularly":[120],"scenarios":[122,165],"complex":[124,182],"distributions":[125],"non-linear":[127],"relationships":[128],"present,":[130],"but":[131],"not":[132],"fully":[133],"understood.":[134],"numerical":[137],"problems":[138],"associated":[139],"normalizing":[141],"logarithmic":[142],"terms,":[143],"we":[144],"follow":[145],"geometric":[147],"approximation":[148],"based":[149],"on":[150],"convex":[152],"hull":[153],"input":[155],"This":[157],"feasible,":[159],"stable,":[160],"accurate":[162],"inference":[163],"involving":[166],"large":[167,180],"amounts":[168],"Numerical":[171],"experiments":[172],"demonstrate":[173],"substantially":[174],"improved":[175],"computational":[176],"efficiency":[177],"when":[178],"handling":[179],"datasets,":[183],"thus":[184],"laying":[185],"foundation":[187],"broad":[190],"range":[191],"applications":[193],"learning":[199],"communities.":[200]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-24T00:00:00"}
