{"id":"https://openalex.org/W2595982264","doi":"https://doi.org/10.1007/s00521-019-04687-8","title":"Multivariate Gaussian and Student-t process regression for multi-output prediction","display_name":"Multivariate Gaussian and Student-t process regression for multi-output prediction","publication_year":2019,"publication_date":"2019-12-31","ids":{"openalex":"https://openalex.org/W2595982264","doi":"https://doi.org/10.1007/s00521-019-04687-8","mag":"2595982264"},"language":"en","primary_location":{"id":"doi:10.1007/s00521-019-04687-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00521-019-04687-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00521-019-04687-8.pdf","source":{"id":"https://openalex.org/S147897268","display_name":"Neural Computing and Applications","issn_l":"0941-0643","issn":["0941-0643","1433-3058"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computing and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00521-019-04687-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087251956","display_name":"Zexun Chen","orcid":"https://orcid.org/0000-0001-9005-7198"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Zexun Chen","raw_affiliation_strings":["Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK","institution_ids":["https://openalex.org/I153648349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100408185","display_name":"Bo Wang","orcid":"https://orcid.org/0000-0003-2012-541X"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Bo Wang","raw_affiliation_strings":["Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK","institution_ids":["https://openalex.org/I153648349"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058069510","display_name":"Alexander N. Gorban","orcid":"https://orcid.org/0000-0001-6224-1430"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alexander N. Gorban","raw_affiliation_strings":["Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK","institution_ids":["https://openalex.org/I153648349"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087251956"],"corresponding_institution_ids":["https://openalex.org/I153648349"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":5.9167,"has_fulltext":true,"cited_by_count":103,"citation_normalized_percentile":{"value":0.96839508,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"32","issue":"8","first_page":"3005","last_page":"3028"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9988999962806702,"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":0.9988999962806702,"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/T11918","display_name":"Forecasting Techniques and Applications","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9797999858856201,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.7542270421981812},{"id":"https://openalex.org/keywords/random-variate","display_name":"Random variate","score":0.6188463568687439},{"id":"https://openalex.org/keywords/multivariate-normal-distribution","display_name":"Multivariate normal distribution","score":0.6046715974807739},{"id":"https://openalex.org/keywords/kriging","display_name":"Kriging","score":0.5762585997581482},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5355638861656189},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5211734175682068},{"id":"https://openalex.org/keywords/multivariate-t-distribution","display_name":"Multivariate t-distribution","score":0.5031561255455017},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4712439179420471},{"id":"https://openalex.org/keywords/marginal-distribution","display_name":"Marginal distribution","score":0.45991674065589905},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34588637948036194},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34570884704589844},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3448604941368103},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.34214144945144653},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3411763906478882},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24597981572151184},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.23218092322349548},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.1853095293045044}],"concepts":[{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.7542270421981812},{"id":"https://openalex.org/C141547133","wikidata":"https://www.wikidata.org/wiki/Q7291996","display_name":"Random variate","level":3,"score":0.6188463568687439},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.6046715974807739},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.5762585997581482},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5355638861656189},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5211734175682068},{"id":"https://openalex.org/C172713675","wikidata":"https://www.wikidata.org/wiki/Q6935144","display_name":"Multivariate t-distribution","level":4,"score":0.5031561255455017},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4712439179420471},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.45991674065589905},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34588637948036194},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34570884704589844},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3448604941368103},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.34214144945144653},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3411763906478882},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24597981572151184},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.23218092322349548},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.1853095293045044},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00521-019-04687-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00521-019-04687-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00521-019-04687-8.pdf","source":{"id":"https://openalex.org/S147897268","display_name":"Neural Computing and Applications","issn_l":"0941-0643","issn":["0941-0643","1433-3058"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computing and Applications","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/6dca66c4-b82b-4a7a-a854-f5c5c49d6c31","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/6dca66c4-b82b-4a7a-a854-f5c5c49d6c31","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Chen, Z, Wang, B & Gorban, A N 2020, 'Multivariate Gaussian and Student-t process regression for multi-output prediction', Neural Computing and Applications, vol. 32, no. 8, pp. 3005-3028. https://doi.org/10.1007/s00521-019-04687-8","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1703.04455","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1703.04455","pdf_url":"https://arxiv.org/pdf/1703.04455","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":null,"raw_type":"text"},{"id":"pmh:oai:figshare.com:article/11387217","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Multivariate_Gaussian_and_Student-t_process_regression_for_multi-output_prediction/11387217","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s00521-019-04687-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00521-019-04687-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00521-019-04687-8.pdf","source":{"id":"https://openalex.org/S147897268","display_name":"Neural Computing and Applications","issn_l":"0941-0643","issn":["0941-0643","1433-3058"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computing and Applications","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","score":0.4300000071525574,"id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2595982264.pdf","grobid_xml":"https://content.openalex.org/works/W2595982264.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1542938076","https://openalex.org/W1550570395","https://openalex.org/W1560081776","https://openalex.org/W1567512734","https://openalex.org/W1584023832","https://openalex.org/W1654787807","https://openalex.org/W1746819321","https://openalex.org/W1816516507","https://openalex.org/W1970157543","https://openalex.org/W1980486587","https://openalex.org/W1981799081","https://openalex.org/W1987913686","https://openalex.org/W2006398000","https://openalex.org/W2040731319","https://openalex.org/W2095654324","https://openalex.org/W2114744608","https://openalex.org/W2117063635","https://openalex.org/W2131668296","https://openalex.org/W2139998722","https://openalex.org/W2142959074","https://openalex.org/W2143266849","https://openalex.org/W2146611938","https://openalex.org/W2154087390","https://openalex.org/W2161767008","https://openalex.org/W2167986580","https://openalex.org/W2178002390","https://openalex.org/W2334018742","https://openalex.org/W2402392025","https://openalex.org/W2605695619","https://openalex.org/W2905148377","https://openalex.org/W2951308445","https://openalex.org/W2963641874","https://openalex.org/W3123404163","https://openalex.org/W3148198191","https://openalex.org/W4206103160","https://openalex.org/W4206212643","https://openalex.org/W4211049957","https://openalex.org/W4230031267"],"related_works":["https://openalex.org/W2018570019","https://openalex.org/W1995261331","https://openalex.org/W3094338031","https://openalex.org/W4390142231","https://openalex.org/W4296275783","https://openalex.org/W1983195306","https://openalex.org/W3176032769","https://openalex.org/W2514951141","https://openalex.org/W2963999324","https://openalex.org/W2057282319"],"abstract_inverted_index":{"Abstract":[0],"Gaussian":[1,27,108],"process":[2,95,109],"model":[3,21,97],"for":[4,13,19,70,99,127,175],"vector-valued":[5],"function":[6],"has":[7,173],"been":[8],"shown":[9,193],"to":[10,23,49,51,62,88,104,194],"be":[11,60],"useful":[12],"multi-output":[14,100],"prediction.":[15,186],"The":[16,152],"existing":[17,118],"method":[18],"this":[20,76,135],"is":[22,36,42,47,84,158],"reformulate":[24,105],"the":[25,68,106,117,128,142,149,155,176,189,200],"matrix-variate":[26,57,71],"distribution":[28],"as":[29,67,146],"a":[30,80,90],"multivariate":[31,64,92,107],"normal":[32],"distribution.":[33,74],"Although":[34],"it":[35],"effective":[37],"in":[38,148,199],"many":[39],"cases,":[40],"reformulation":[41],"not":[43,55,86],"always":[44],"workable":[45],"and":[46,122,131,138,163,183],"difficult":[48],"apply":[50],"other":[52],"distributions":[53,58,133],"because":[54],"all":[56],"can":[59,140],"transformed":[61],"respective":[63],"distributions,":[65],"such":[66],"case":[69],"Student-":[72,93],"t":[73,94],"In":[75,166],"paper,":[77],"we":[78,168],"propose":[79],"unified":[81,136],"framework":[82,137],"which":[83],"used":[85,147],"only":[87],"introduce":[89],"novel":[91],"regression":[96,110],"(MV-TPR)":[98],"prediction,":[101],"but":[102],"also":[103],"(MV-GPR)":[111],"that":[112,171],"overcomes":[113],"some":[114],"limitations":[115],"of":[116,154],"methods.":[119],"Both":[120],"MV-GPR":[121],"MV-TPR":[123,172],"have":[124],"closed-form":[125],"expressions":[126],"marginal":[129],"likelihoods":[130],"predictive":[132],"under":[134],"thus":[139],"adopt":[141],"same":[143],"optimization":[144],"approaches":[145],"conventional":[150],"GPR.":[151],"usefulness":[153],"proposed":[156,190],"methods":[157,191],"illustrated":[159],"through":[160],"several":[161],"simulated":[162],"real-data":[164],"examples.":[165],"particular,":[167],"verify":[169],"empirically":[170],"superiority":[174],"datasets":[177],"considered,":[178],"including":[179],"air":[180],"quality":[181],"prediction":[182],"bike":[184],"rent":[185],"At":[187],"last,":[188],"are":[192],"produce":[195],"profitable":[196],"investment":[197],"strategies":[198],"stock":[201],"markets.":[202]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":21},{"year":2023,"cited_by_count":24},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2020-11-23T00:00:00"}