{"id":"https://openalex.org/W7147035535","doi":"https://doi.org/10.48550/arxiv.2603.27672","title":"Energy Score-Guided Neural Gaussian Mixture Model for Predictive Uncertainty Quantification","display_name":"Energy Score-Guided Neural Gaussian Mixture Model for Predictive Uncertainty Quantification","publication_year":2026,"publication_date":"2026-03-29","ids":{"openalex":"https://openalex.org/W7147035535","doi":"https://doi.org/10.48550/arxiv.2603.27672"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.27672","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.27672","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.2603.27672","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132716518","display_name":"Yang Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049157841","display_name":"Chunlin Ji","orcid":"https://orcid.org/0000-0003-2260-4107"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ji, Chunlin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132635856","display_name":"Haoyang Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Haoyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5132651725","display_name":"Ke Deng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Deng, Ke","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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.7756999731063843,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.7756999731063843,"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":0.06459999829530716,"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":0.03869999945163727,"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/robustness","display_name":"Robustness (evolution)","score":0.6935999989509583},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.6442000269889832},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.567799985408783},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.545199990272522},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.5418000221252441},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5271000266075134},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5063999891281128},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.45339998602867126},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.44690001010894775}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6935999989509583},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.6442000269889832},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6018999814987183},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.567799985408783},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.545199990272522},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5432000160217285},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.5418000221252441},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5271000266075134},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5063999891281128},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.47870001196861267},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.45339998602867126},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.44690001010894775},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.43230000138282776},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4000999927520752},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.3862000107765198},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.3474999964237213},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3325999975204468},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3203999996185303},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.3043000102043152},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C56672385","wikidata":"https://www.wikidata.org/wiki/Q17157111","display_name":"Mixture distribution","level":3,"score":0.2897999882698059},{"id":"https://openalex.org/C45804977","wikidata":"https://www.wikidata.org/wiki/Q7239673","display_name":"Predictive modelling","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.27250000834465027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25699999928474426}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.27672","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.27672","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.2603.27672","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.27672","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Quantifying":[0],"predictive":[1,90,180],"uncertainty":[2,91,183],"is":[3],"essential":[4],"for":[5],"real":[6,168],"world":[7,169],"machine":[8],"learning":[9],"applications,":[10],"especially":[11],"in":[12,115,176],"scenarios":[13],"requiring":[14],"reliable":[15],"and":[16,46,56,104,142,167,182],"interpretable":[17],"predictions.":[18],"Many":[19],"common":[20],"parametric":[21],"approaches":[22],"rely":[23],"on":[24,159,164],"neural":[25],"networks":[26],"to":[27,50,88,99,110],"estimate":[28],"distribution":[29],"parameters":[30],"by":[31],"optimizing":[32],"the":[33,54,59,68,95,106,122,127,138,149,172],"negative":[34],"log":[35],"likelihood.":[36],"However,":[37],"these":[38],"methods":[39],"often":[40],"encounter":[41],"challenges":[42],"like":[43],"training":[44],"instability":[45],"mode":[47],"collapse,":[48],"leading":[49],"poor":[51],"estimates":[52],"of":[53,58,97,108,129,174,178],"mean":[55],"variance":[57],"target":[60],"output":[61],"distribution.":[62],"In":[63],"this":[64],"work,":[65],"we":[66],"propose":[67],"Neural":[69],"Energy":[70,85],"Gaussian":[71,80],"Mixture":[72,81],"Model":[73,82],"(NE-GMM),":[74],"a":[75,130],"novel":[76],"framework":[77],"that":[78,121,148],"integrates":[79],"(GMM)":[83],"with":[84,137,155],"Score":[86],"(ES)":[87],"enhance":[89],"quantification.":[92,184],"NE-GMM":[93,175],"leverages":[94,105],"flexibility":[96],"GMM":[98],"capture":[100],"complex":[101],"multimodal":[102],"distributions":[103],"robustness":[107],"ES":[109],"ensure":[111],"well":[112],"calibrated":[113],"predictions":[114],"diverse":[116],"scenarios.":[117],"We":[118],"theoretically":[119],"prove":[120],"hybrid":[123],"loss":[124],"function":[125],"satisfies":[126],"properties":[128],"strictly":[131],"proper":[132],"scoring":[133],"rule,":[134],"ensuring":[135],"alignment":[136],"true":[139],"data":[140],"distribution,":[141],"establish":[143],"generalization":[144],"error":[145],"bounds,":[146],"demonstrating":[147],"model's":[150],"empirical":[151],"performance":[152,158],"closely":[153],"aligns":[154],"its":[156],"expected":[157],"unseen":[160],"data.":[161],"Extensive":[162],"experiments":[163],"both":[165,179],"synthetic":[166],"datasets":[170],"demonstrate":[171],"superiority":[173],"terms":[177],"accuracy":[181]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-02T00:00:00"}
