{"id":"https://openalex.org/W7082657045","doi":"https://doi.org/10.48550/arxiv.2509.15244","title":"Kernel Model Validation: How To Do It, And Why You Should Care","display_name":"Kernel Model Validation: How To Do It, And Why You Should Care","publication_year":2025,"publication_date":"2025-09-17","ids":{"openalex":"https://openalex.org/W7082657045","doi":"https://doi.org/10.48550/arxiv.2509.15244"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2509.15244","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.15244","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.2509.15244","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Graziani, Carlo","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Graziani, Carlo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Ngom, Marieme","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ngom, Marieme","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"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":true,"primary_topic":{"id":"https://openalex.org/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.6625999808311462,"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/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.6625999808311462,"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/T13067","display_name":"Geological Modeling and Analysis","score":0.030799999833106995,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14311","display_name":"Electrical and Electromagnetic Research","score":0.01940000057220459,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.635699987411499},{"id":"https://openalex.org/keywords/calibration","display_name":"Calibration","score":0.5633999705314636},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5324000120162964},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.5266000032424927},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.5044999718666077},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.460099995136261},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4253999888896942},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4097000062465668},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.39410001039505005},{"id":"https://openalex.org/keywords/kriging","display_name":"Kriging","score":0.3864000141620636}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.635699987411499},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5703999996185303},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.5633999705314636},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5340999960899353},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5324000120162964},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.5266000032424927},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.5044999718666077},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.460099995136261},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4253999888896942},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4140999913215637},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4097000062465668},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.39410001039505005},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.3864000141620636},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.36910000443458557},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3675000071525574},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.3578999936580658},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.35249999165534973},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3199999928474426},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31380000710487366},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.3077999949455261},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C176147448","wikidata":"https://www.wikidata.org/wiki/Q1889114","display_name":"Sensitivity analysis","level":3,"score":0.3012000024318695},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C177803969","wikidata":"https://www.wikidata.org/wiki/Q29205","display_name":"Uncertainty analysis","level":2,"score":0.2888000011444092},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.2831000089645386},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C143017306","wikidata":"https://www.wikidata.org/wiki/Q3318133","display_name":"Probabilistic relevance model","level":4,"score":0.27399998903274536},{"id":"https://openalex.org/C137209882","wikidata":"https://www.wikidata.org/wiki/Q1403517","display_name":"Measurement uncertainty","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C203223496","wikidata":"https://www.wikidata.org/wiki/Q4681344","display_name":"Additive model","level":2,"score":0.25270000100135803},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2509.15244","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.15244","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.2509.15244","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.15244","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Gaussian":[0],"Process":[1],"(GP)":[2],"models":[3],"are":[4],"popular":[5],"tools":[6],"in":[7,44,89,107],"uncertainty":[8,17,59,105],"quantification":[9],"(UQ)":[10],"because":[11],"they":[12],"purport":[13],"to":[14,23,31,39,114,150],"furnish":[15],"functional":[16],"estimates":[18,60],"that":[19,125],"can":[20,84],"be":[21],"used":[22],"represent":[24],"model":[25],"uncertainty.":[26],"It":[27],"is":[28,47,61],"often":[29],"difficult":[30],"state":[32],"with":[33,148],"precision":[34],"what":[35,45],"probabilistic":[36,72],"interpretation":[37,102],"attaches":[38],"such":[40,51,58],"an":[41],"uncertainty,":[42],"and":[43,64,109,144],"way":[46],"it":[48],"calibrated.":[49],"Without":[50],"a":[52,90,118],"calibration":[53,73,82],"statement,":[54],"the":[55,68,101,127,146],"value":[56],"of":[57,70,74,103,131,138],"quite":[62],"limited":[63],"qualitative.":[65],"We":[66,99,134],"motivate":[67],"importance":[69],"proper":[71],"GP":[75,80,132,139],"predictions":[76],"by":[77],"describing":[78],"how":[79,110],"predictive":[81],"failures":[83],"cause":[85],"degraded":[86],"convergence":[87],"properties":[88],"target":[91],"optimization":[92],"algorithm":[93],"called":[94],"Targeted":[95],"Adaptive":[96],"Design":[97],"(TAD).":[98],"discuss":[100,145],"GP-generated":[104],"intervals":[106],"UQ,":[108],"one":[111],"may":[112],"learn":[113],"trust":[115],"them,":[116],"through":[117],"formal":[119],"procedure":[120],"for":[121],"covariance":[122],"kernel":[123],"validation":[124],"exploits":[126],"multivariate":[128],"normal":[129],"nature":[130],"predictions.":[133],"give":[135],"simple":[136],"examples":[137],"regression":[140],"misspecified":[141],"1-dimensional":[142],"models,":[143],"situation":[147],"respect":[149],"higher-dimensional":[151],"models.":[152]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}
