{"id":"https://openalex.org/W1543474109","doi":"https://doi.org/10.5555/1953048.2021067","title":"Information Rates of Nonparametric Gaussian Process Methods","display_name":"Information Rates of Nonparametric Gaussian Process Methods","publication_year":2011,"publication_date":"2011-02-01","ids":{"openalex":"https://openalex.org/W1543474109","doi":"https://doi.org/10.5555/1953048.2021067","mag":"1543474109"},"language":"en","primary_location":{"id":"pmh:oai:research.vu.nl:publications/7d6b9940-246a-4c74-8d3d-31bf1d1a9980","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/7d6b9940-246a-4c74-8d3d-31bf1d1a9980","pdf_url":"https://research.vu.nl/ws/files/3083751/284224.pdf","source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"van der Vaart, A W & Zanten, J H 2011, 'Information rates of nonparametric Gaussian process methods', Journal of Machine Learning Research, vol. 12, pp. 2-95-2119.","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.vu.nl/ws/files/3083751/284224.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015126561","display_name":"Aad van der Vaart","orcid":"https://orcid.org/0000-0002-8074-2375"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aad van der Vaart","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8074-2375","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037310336","display_name":"Harry van Zanten","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Harry van Zanten","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":8.4358,"has_fulltext":true,"cited_by_count":131,"citation_normalized_percentile":{"value":0.97336831,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"12","issue":"60","first_page":"2095","last_page":"2119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9998999834060669,"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":0.9998999834060669,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11236","display_name":"Control Systems and Identification","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7087435722351074},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7003450989723206},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.663806676864624},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.6515151262283325},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5380356907844543},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.5282451510429382},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.5220856070518494},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5133265852928162},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4793879985809326},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41074222326278687},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.3704809248447418},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3275664150714874},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10236391425132751}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7087435722351074},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7003450989723206},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.663806676864624},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.6515151262283325},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5380356907844543},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.5282451510429382},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.5220856070518494},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5133265852928162},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4793879985809326},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41074222326278687},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.3704809248447418},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3275664150714874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10236391425132751},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:research.vu.nl:publications/7d6b9940-246a-4c74-8d3d-31bf1d1a9980","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/7d6b9940-246a-4c74-8d3d-31bf1d1a9980","pdf_url":"https://research.vu.nl/ws/files/3083751/284224.pdf","source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"van der Vaart, A W & Zanten, J H 2011, 'Information rates of nonparametric Gaussian process methods', Journal of Machine Learning Research, vol. 12, pp. 2-95-2119.","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.415.5732","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.415.5732","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://jmlr.org/papers/volume12/vandervaart11a/vandervaart11a.pdf","raw_type":"text"},{"id":"mag:1543474109","is_oa":false,"landing_page_url":"http://jmlr.csail.mit.edu/papers/volume12/vandervaart11a/vandervaart11a.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S118988714","display_name":"Journal of Machine Learning Research","issn_l":"1532-4435","issn":["1532-4435","1533-7928"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718","https://openalex.org/P4310316440"],"host_organization_lineage_names":["The MIT Press","Massachusetts Institute of Technology"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Journal of Machine Learning Research","raw_type":null}],"best_oa_location":{"id":"pmh:oai:research.vu.nl:publications/7d6b9940-246a-4c74-8d3d-31bf1d1a9980","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/7d6b9940-246a-4c74-8d3d-31bf1d1a9980","pdf_url":"https://research.vu.nl/ws/files/3083751/284224.pdf","source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"van der Vaart, A W & Zanten, J H 2011, 'Information rates of nonparametric Gaussian process methods', Journal of Machine Learning Research, vol. 12, pp. 2-95-2119.","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1543474109.pdf","grobid_xml":"https://content.openalex.org/works/W1543474109.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W61851564","https://openalex.org/W603748733","https://openalex.org/W1489087445","https://openalex.org/W1509689762","https://openalex.org/W1511694993","https://openalex.org/W1528907134","https://openalex.org/W1577469824","https://openalex.org/W1580561995","https://openalex.org/W1667961663","https://openalex.org/W1746819321","https://openalex.org/W1974046151","https://openalex.org/W2010353172","https://openalex.org/W2014777867","https://openalex.org/W2045904249","https://openalex.org/W2056963858","https://openalex.org/W2062532221","https://openalex.org/W2067539122","https://openalex.org/W2107829755","https://openalex.org/W2126417278","https://openalex.org/W2133255100","https://openalex.org/W2157596407","https://openalex.org/W3104936529","https://openalex.org/W3105422985"],"related_works":["https://openalex.org/W2126417278","https://openalex.org/W1746819321","https://openalex.org/W1528907134","https://openalex.org/W2157596407","https://openalex.org/W2018044188","https://openalex.org/W2062532221","https://openalex.org/W3105422985","https://openalex.org/W3104051756","https://openalex.org/W2168464387","https://openalex.org/W2038845890","https://openalex.org/W1698155719","https://openalex.org/W1486164486","https://openalex.org/W2042799176","https://openalex.org/W1974046151","https://openalex.org/W1486811909","https://openalex.org/W55912154","https://openalex.org/W1986280275","https://openalex.org/W1973333099","https://openalex.org/W1565176583","https://openalex.org/W1562147356"],"abstract_inverted_index":{"We":[0,24,68],"consider":[1],"the":[2,21,27,31,42,46,65,70,73,77,86,90,102,110,129,136,139,144,147],"quality":[3],"of":[4,30,64,72,112,138,146],"learning":[5,32],"a":[6,10,15,123],"response":[7,22,99,114,149],"function":[8,115],"by":[9],"nonparametric":[11],"Bayesian":[12],"approach":[13],"using":[14],"Gaussian":[16,117],"process":[17],"(GP)":[18],"prior":[19,141],"on":[20,41,109],"function.":[23,126,150],"upper":[25,39,53,74],"bound":[26,40,54,75],"quadratic":[28],"risk":[29],"procedure,":[33],"which":[34,105],"in":[35,57,122],"turn":[36],"is":[37,55,120],"an":[38],"Kullback-Leibler":[43],"information":[44,91],"between":[45],"predictive":[47],"and":[48,61,79,88,116,119],"true":[49,113],"data":[50],"distribution.":[51],"The":[52],"expressed":[56],"small":[58],"ball":[59],"probabilities":[60],"concentration":[62,125],"measures":[63],"GP":[66,140],"prior.":[67],"illustrate":[69],"computation":[71],"for":[76,96,133],"Mat\u00e9rn":[78],"squared":[80],"exponential":[81],"kernels.":[82],"For":[83],"these":[84],"priors":[85],"risk,":[87],"hence":[89],"criterion,":[92],"tends":[93],"to":[94],"zero":[95],"all":[97],"continuous":[98],"functions.":[100],"However,":[101],"rate":[103],"at":[104],"this":[106],"happens":[107],"depends":[108],"combination":[111],"prior,":[118],"expressible":[121],"certain":[124],"In":[127],"particular,":[128],"results":[130],"show":[131],"that":[132],"good":[134],"performance,":[135],"regularity":[137,145],"should":[142],"match":[143],"unknown":[148]},"counts_by_year":[{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}