{"id":"https://openalex.org/W7140198961","doi":"https://doi.org/10.48550/arxiv.2603.20655","title":"Exponential Family Discriminant Analysis: Generalizing LDA-Style Generative Classification to Non-Gaussian Models","display_name":"Exponential Family Discriminant Analysis: Generalizing LDA-Style Generative Classification to Non-Gaussian Models","publication_year":2026,"publication_date":"2026-03-21","ids":{"openalex":"https://openalex.org/W7140198961","doi":"https://doi.org/10.48550/arxiv.2603.20655"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.20655","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20655","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.2603.20655","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Lakkapragada, Anish","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lakkapragada, Anish","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"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/T10136","display_name":"Statistical Methods and Inference","score":0.13410000503063202,"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/T10136","display_name":"Statistical Methods and Inference","score":0.13410000503063202,"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/T11652","display_name":"Imbalanced Data Classification Techniques","score":0.11159999668598175,"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/T13748","display_name":"Advanced Statistical Modeling Techniques","score":0.11050000041723251,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/estimator","display_name":"Estimator","score":0.6884999871253967},{"id":"https://openalex.org/keywords/exponential-family","display_name":"Exponential family","score":0.5860000252723694},{"id":"https://openalex.org/keywords/linear-discriminant-analysis","display_name":"Linear discriminant analysis","score":0.5214999914169312},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.47780001163482666},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.43560001254081726},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.3898000121116638},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.36649999022483826},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.34880000352859497},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.34220001101493835}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7038000226020813},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6884999871253967},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.5860000252723694},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5523999929428101},{"id":"https://openalex.org/C69738355","wikidata":"https://www.wikidata.org/wiki/Q1228929","display_name":"Linear discriminant analysis","level":2,"score":0.5214999914169312},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.47780001163482666},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.43560001254081726},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.3898000121116638},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.34880000352859497},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3278000056743622},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.31209999322891235},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.2976999878883362},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.29409998655319214},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.28450000286102295},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27469998598098755},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.27320000529289246},{"id":"https://openalex.org/C84839998","wikidata":"https://www.wikidata.org/wiki/Q5249245","display_name":"Decision rule","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26350000500679016},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C2780617739","wikidata":"https://www.wikidata.org/wiki/Q4680738","display_name":"Adaptive estimator","level":3,"score":0.25949999690055847}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.20655","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20655","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.2603.20655","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20655","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":[{"score":0.6929709911346436,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,79,157],"introduce":[1],"Exponential":[2],"Family":[3],"Discriminant":[4,15],"Analysis":[5,16],"(EFDA),":[6],"a":[7,38,53,66,136],"unified":[8],"generative":[9],"framework":[10],"that":[11,32,56,81,138,163],"extends":[12],"classical":[13],"Linear":[14],"(LDA)":[17],"beyond":[18],"the":[19,26,30,60,75,119,168,176],"Gaussian":[20],"setting":[21],"to":[22,37,96,187],"any":[23],"member":[24],"of":[25,122],"exponential":[27,40],"family.":[28],"Under":[29],"assumption":[31],"each":[33],"class-conditional":[34],"density":[35],"belongs":[36],"common":[39],"family,":[41],"EFDA":[42,82,117],"derives":[43],"closed-form":[44],"maximum-likelihood":[45],"estimators":[46],"for":[47,143,193],"all":[48,144,148,200,218],"natural":[49],"parameters":[50],"and":[51,69,86,92,101,125,146,160,174,210],"yields":[52],"decision":[54,72],"rule":[55],"is":[57,83,139,175],"linear":[58],"in":[59,74,179,204],"sufficient":[61],"statistic,":[62],"recovering":[63],"LDA":[64],"as":[65,214],"special":[67],"case":[68],"capturing":[70],"nonlinear":[71],"boundaries":[73],"original":[76],"feature":[77],"space.":[78],"prove":[80,159],"asymptotically":[84,155],"calibrated":[85],"statistically":[87],"efficient":[88],"under":[89,171],"correct":[90,172],"specification,":[91,173],"we":[93,197],"generalise":[94],"it":[95,141],"$K":[97],"\\geq":[98],"2$":[99],"classes":[100],"multivariate":[102],"data.":[103],"Through":[104],"extensive":[105],"simulation":[106],"across":[107,147],"five":[108],"exponential-family":[109],"distributions":[110],"(Weibull,":[111],"Gamma,":[112],"Exponential,":[113],"Poisson,":[114],"Negative":[115],"Binomial),":[116],"matches":[118],"classification":[120],"accuracy":[121],"LDA,":[123],"QDA,":[124],"logistic":[126],"regression":[127],"while":[128],"reducing":[129],"Expected":[130],"Calibration":[131],"Error":[132],"(ECE)":[133],"by":[134,222],"$2$-$6\\times$,":[135],"gap":[137],"structural:":[140],"persists":[142],"$n$":[145],"class-imbalance":[149],"levels,":[150],"because":[151],"misspecified":[152],"models":[153],"remain":[154],"miscalibrated.":[156],"further":[158],"empirically":[161],"confirm":[162],"EFDA's":[164],"log-odds":[165],"estimator":[166,178],"approaches":[167],"Cram\u00e9r-Rao":[169],"bound":[170],"only":[177],"our":[180],"comparison":[181],"whose":[182],"mean":[183],"squared":[184],"error":[185],"converges":[186],"zero.":[188],"Complete":[189],"derivations":[190],"are":[191],"provided":[192],"nine":[194],"distributions.":[195],"Finally,":[196],"formally":[198],"verify":[199],"four":[201],"theoretical":[202],"propositions":[203],"Lean":[205],"4,":[206],"using":[207],"Aristotle":[208],"(Harmonic)":[209],"OpenGauss":[211],"(Math,":[212],"Inc.)":[213],"proof":[215],"generators,":[216],"with":[217],"outputs":[219],"independently":[220],"machine-checked":[221],"AXLE":[223],"(Axiom).":[224]},"counts_by_year":[],"updated_date":"2026-03-26T06:05:38.182114","created_date":"2026-03-25T00:00:00"}
