{"id":"https://openalex.org/W4280637583","doi":"https://doi.org/10.48550/arxiv.2205.07764","title":"On the inability of Gaussian process regression to optimally learn compositional functions","display_name":"On the inability of Gaussian process regression to optimally learn compositional functions","publication_year":2022,"publication_date":"2022-05-16","ids":{"openalex":"https://openalex.org/W4280637583","doi":"https://doi.org/10.48550/arxiv.2205.07764"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2205.07764","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2205.07764","pdf_url":"https://arxiv.org/pdf/2205.07764","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2205.07764","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074287730","display_name":"Matteo Giordano","orcid":"https://orcid.org/0000-0003-1581-1706"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Giordano, Matteo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051724436","display_name":"Kolyan Ray","orcid":"https://orcid.org/0000-0002-2874-092X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ray, Kolyan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002981992","display_name":"Johannes Schmidt-Hieber","orcid":"https://orcid.org/0000-0003-2699-4990"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schmidt-Hieber, Johannes","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074287730"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":7,"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":0.9983999729156494,"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":0.9983999729156494,"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/T11324","display_name":"Spectroscopy Techniques in Biomedical and Chemical Research","score":0.9807999730110168,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.9539999961853027,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.7312576770782471},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.7166461944580078},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.7043321132659912},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.657866895198822},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6060991287231445},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5642213821411133},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.47901028394699097},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44294169545173645},{"id":"https://openalex.org/keywords/kriging","display_name":"Kriging","score":0.42934268712997437},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33331650495529175},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33218473196029663},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.30764052271842957}],"concepts":[{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.7312576770782471},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.7166461944580078},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7043321132659912},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.657866895198822},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6060991287231445},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5642213821411133},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.47901028394699097},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44294169545173645},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.42934268712997437},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33331650495529175},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33218473196029663},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.30764052271842957},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"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:arXiv.org:2205.07764","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2205.07764","pdf_url":"https://arxiv.org/pdf/2205.07764","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:ris.utwente.nl:openaire/4f254da7-6d62-4bb7-9232-b6cd9ed0428a","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/4f254da7-6d62-4bb7-9232-b6cd9ed0428a","pdf_url":"https://ris.utwente.nl/ws/files/460201210/2205.07764v2.pdf","source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Giordano, M, Ray, K & Schmidt-Hieber, J 2022 'On the inability of Gaussian process regression to optimally learn compositional functions' ArXiv.org. https://doi.org/10.48550/arXiv.2205.07764","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2205.07764","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2205.07764","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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2205.07764","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2205.07764","pdf_url":"https://arxiv.org/pdf/2205.07764","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W566010457","https://openalex.org/W2600092203","https://openalex.org/W4293503520","https://openalex.org/W4300066510","https://openalex.org/W2056958800","https://openalex.org/W2803685231","https://openalex.org/W3134152097","https://openalex.org/W4311388919","https://openalex.org/W2966696655","https://openalex.org/W2115519811"],"abstract_inverted_index":{"We":[0,42],"rigorously":[1],"prove":[2],"that":[3,44,71,82],"deep":[4],"Gaussian":[5,10,34,61],"process":[6,11,35,62],"priors":[7,12],"can":[8,63],"outperform":[9],"if":[13,45],"the":[14,46,55,66,76,87],"target":[15],"function":[16,48],"has":[17],"a":[18,38,50,69,80],"compositional":[19],"structure.":[20],"To":[21],"this":[22],"end,":[23],"we":[24],"study":[25],"information-theoretic":[26],"lower":[27],"bounds":[28],"for":[29,33],"posterior":[30,56],"contraction":[31],"rates":[32],"regression":[36,40],"in":[37,86],"continuous":[39],"model.":[41],"show":[43],"true":[47],"is":[49,72,83],"generalized":[51],"additive":[52],"function,":[53],"then":[54],"based":[57],"on":[58],"any":[59],"mean-zero":[60],"only":[64],"recover":[65],"truth":[67],"at":[68],"rate":[70,78],"strictly":[73],"slower":[74],"than":[75],"minimax":[77],"by":[79],"factor":[81],"polynomially":[84],"suboptimal":[85],"sample":[88],"size":[89],"$n$.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-17T09:09:15.849793","created_date":"2022-05-22T00:00:00"}
