{"id":"https://openalex.org/W4403590075","doi":"https://doi.org/10.48550/arxiv.2409.03953","title":"Epistemic Uncertainty and Observation Noise with the Neural Tangent Kernel","display_name":"Epistemic Uncertainty and Observation Noise with the Neural Tangent Kernel","publication_year":2024,"publication_date":"2024-09-06","ids":{"openalex":"https://openalex.org/W4403590075","doi":"https://doi.org/10.48550/arxiv.2409.03953"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2409.03953","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.03953","pdf_url":"https://arxiv.org/pdf/2409.03953","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2409.03953","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093887382","display_name":"Sergio Calvo-Ordo\u00f1ez","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Calvo-Ordo\u00f1ez, Sergio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027774255","display_name":"Konstantina Palla","orcid":"https://orcid.org/0000-0001-7066-0539","observed_orcids":["https://orcid.org/0000-0001-7066-0539"]},"institutions":[{"id":"https://openalex.org/I4401726855","display_name":"Spotify (Sweden)","ror":"https://ror.org/00hbd6420","country_code":"SE","type":"company","lineage":["https://openalex.org/I4401726855"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Palla, Konstantina","raw_affiliation_strings":["Spotify"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Spotify","institution_ids":["https://openalex.org/I4401726855"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043239539","display_name":"Kamil Ciosek","orcid":"https://orcid.org/0000-0002-0238-9393","observed_orcids":["https://orcid.org/0000-0002-0238-9393"]},"institutions":[{"id":"https://openalex.org/I4401726855","display_name":"Spotify (Sweden)","ror":"https://ror.org/00hbd6420","country_code":"SE","type":"company","lineage":["https://openalex.org/I4401726855"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Ciosek, Kamil","raw_affiliation_strings":["Spotify"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Spotify","institution_ids":["https://openalex.org/I4401726855"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9984999895095825,"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":0.9984999895095825,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.0003000000142492354,"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/T10320","display_name":"Neural Networks and Applications","score":0.0003000000142492354,"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/neural-tangent-kernel","display_name":"neural tangent kernel","score":0.9380000233650208},{"id":"https://openalex.org/keywords/epistemic-uncertainty","display_name":"epistemic uncertainty","score":0.9909999966621399},{"id":"https://openalex.org/keywords/measurement-noise","display_name":"measurement noise","score":0.875},{"id":"https://openalex.org/keywords/gaussian-process-approximation","display_name":"Gaussian process approximation","score":0.48100000619888306},{"id":"https://openalex.org/keywords/wide-neural-networks","display_name":"wide neural networks","score":0.890999972820282},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"gradient descent","score":0.5400000214576721}],"concepts":[{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.7133559584617615},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6557544469833374},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6010363698005676},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4529144763946533},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.45164912939071655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4228588342666626},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.42011094093322754},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3359133005142212},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2401646077632904},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13050946593284607},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2409.03953","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.03953","pdf_url":"https://arxiv.org/pdf/2409.03953","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2409.03953","doi":"https://doi.org/10.48550/arxiv.2409.03953","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2409.03953","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2409.03953","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.03953","pdf_url":"https://arxiv.org/pdf/2409.03953","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403590075.pdf","grobid_xml":"https://content.openalex.org/works/W4403590075.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1959608418","https://openalex.org/W2899205164","https://openalex.org/W2977953007","https://openalex.org/W3102512603","https://openalex.org/W4293819916"],"related_works":["https://openalex.org/W4407184391","https://openalex.org/W4407212482","https://openalex.org/W4406733553","https://openalex.org/W3102512603","https://openalex.org/W7147137741","https://openalex.org/W7030111079","https://openalex.org/W2898622970","https://openalex.org/W4415032490","https://openalex.org/W4402963657","https://openalex.org/W2739429571"],"abstract_inverted_index":{"Recent":[0],"work":[1],"has":[2],"shown":[3],"that":[4],"training":[5,86,91],"wide":[6],"neural":[7],"networks":[8],"with":[9,28,59,84],"gradient":[10,99],"descent":[11,100],"is":[12],"formally":[13],"equivalent":[14],"to":[15,57],"computing":[16],"the":[17,20,29,35,69,109],"mean":[18,103],"of":[19,95,111],"posterior":[21,70],"distribution":[22],"in":[23,50],"a":[24,74,92,102],"Gaussian":[25],"Process":[26],"(GP)":[27],"Neural":[30],"Tangent":[31],"Kernel":[32],"(NTK)":[33],"as":[34,88],"prior":[36],"covariance":[37],"and":[38],"zero":[39],"aleatoric":[40,61],"noise":[41],"\\parencite{jacot2018neural}.":[42],"In":[43],"this":[44,48],"paper,":[45],"we":[46,54,64],"extend":[47],"framework":[49],"two":[51],"ways.":[52],"First,":[53],"show":[55],"how":[56],"deal":[58],"non-zero":[60],"noise.":[62],"Second,":[63],"derive":[65],"an":[66],"estimator":[67],"for":[68],"covariance,":[71],"giving":[72],"us":[73],"handle":[75],"on":[76,101,117],"epistemic":[77],"uncertainty.":[78],"Our":[79],"proposed":[80],"approach":[81],"integrates":[82],"seamlessly":[83],"standard":[85],"pipelines,":[87],"it":[89],"involves":[90],"small":[93],"number":[94],"additional":[96],"predictors":[97],"using":[98],"squared":[104],"error":[105],"loss.":[106],"We":[107],"demonstrate":[108],"proof-of-concept":[110],"our":[112],"method":[113],"through":[114],"empirical":[115],"evaluation":[116],"synthetic":[118],"regression.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2024-10-22T00:00:00"}