{"id":"https://openalex.org/W3042111838","doi":"https://doi.org/10.1109/mlsp49062.2020.9231560","title":"Fast Variational Learning in State-Space Gaussian Process Models","display_name":"Fast Variational Learning in State-Space Gaussian Process Models","publication_year":2020,"publication_date":"2020-09-01","ids":{"openalex":"https://openalex.org/W3042111838","doi":"https://doi.org/10.1109/mlsp49062.2020.9231560","mag":"3042111838"},"language":"en","primary_location":{"id":"doi:10.1109/mlsp49062.2020.9231560","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mlsp49062.2020.9231560","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2007.04731","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059273023","display_name":"Paul E. Chang","orcid":null},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Paul E. Chang","raw_affiliation_strings":["Aalto University, Espoo, Finland","Aalto University; Espoo Finland"],"affiliations":[{"raw_affiliation_string":"Aalto University, Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Aalto University; Espoo Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067821485","display_name":"William J. Wilkinson","orcid":null},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"William J. Wilkinson","raw_affiliation_strings":["Aalto University, Espoo, Finland","Aalto University; Espoo Finland"],"affiliations":[{"raw_affiliation_string":"Aalto University, Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Aalto University; Espoo Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053565482","display_name":"Mohammad Emtiyaz Khan","orcid":"https://orcid.org/0000-0001-7614-0489"},"institutions":[{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Mohammad Emtiyaz Khan","raw_affiliation_strings":["RIKEN Center for AI Project, Tokyo, Japan","RIKEN Center for AI Project,Tokyo,Japan"],"affiliations":[{"raw_affiliation_string":"RIKEN Center for AI Project, Tokyo, Japan","institution_ids":["https://openalex.org/I4210126580"]},{"raw_affiliation_string":"RIKEN Center for AI Project,Tokyo,Japan","institution_ids":["https://openalex.org/I4210126580"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014200248","display_name":"Arno Solin","orcid":"https://orcid.org/0000-0002-0958-7886"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Arno Solin","raw_affiliation_strings":["Aalto University, Espoo, Finland","Aalto University; Espoo Finland"],"affiliations":[{"raw_affiliation_string":"Aalto University, Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Aalto University; Espoo Finland","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5059273023"],"corresponding_institution_ids":["https://openalex.org/I9927081"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07764792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":null,"first_page":"1","last_page":"6"},"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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9731000065803528,"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/T11236","display_name":"Control Systems and Identification","score":0.9688000082969666,"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/inference","display_name":"Inference","score":0.7473028898239136},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.6754468679428101},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5988484025001526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5986020565032959},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5021874904632568},{"id":"https://openalex.org/keywords/expectation-propagation","display_name":"Expectation propagation","score":0.5007138252258301},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.495978444814682},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.47372546792030334},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46536970138549805},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4612390697002411},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4592655897140503},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44987618923187256},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.434174507856369},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31237226724624634},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20659282803535461},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0833272635936737}],"concepts":[{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.7473028898239136},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.6754468679428101},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5988484025001526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5986020565032959},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5021874904632568},{"id":"https://openalex.org/C2779363554","wikidata":"https://www.wikidata.org/wiki/Q5420835","display_name":"Expectation propagation","level":4,"score":0.5007138252258301},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.495978444814682},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.47372546792030334},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46536970138549805},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4612390697002411},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4592655897140503},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44987618923187256},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.434174507856369},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31237226724624634},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20659282803535461},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0833272635936737},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/mlsp49062.2020.9231560","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mlsp49062.2020.9231560","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2007.04731","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.04731","pdf_url":"https://arxiv.org/pdf/2007.04731","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":"mag:3042111838","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2007.04731.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2007.04731","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2007.04731","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"},{"id":"doi:10.17023/c58b-4n29","is_oa":true,"landing_page_url":"https://doi.org/10.17023/c58b-4n29","pdf_url":null,"source":{"id":"https://openalex.org/S7407051697","display_name":"IEEE RESOURCE CENTERS","issn_l":null,"issn":[],"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":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:2007.04731","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.04731","pdf_url":"https://arxiv.org/pdf/2007.04731","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3042111838.pdf","grobid_xml":"https://content.openalex.org/works/W3042111838.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W88520345","https://openalex.org/W1533660737","https://openalex.org/W2036084078","https://openalex.org/W2157826563","https://openalex.org/W2787723410","https://openalex.org/W2915071561","https://openalex.org/W2940934113","https://openalex.org/W2962726118","https://openalex.org/W2962791800","https://openalex.org/W3034295561","https://openalex.org/W3037093830","https://openalex.org/W4232464081","https://openalex.org/W6631732945","https://openalex.org/W6683442033","https://openalex.org/W6735905430","https://openalex.org/W6749099202","https://openalex.org/W6759138944","https://openalex.org/W6772154186","https://openalex.org/W6779347534"],"related_works":["https://openalex.org/W2916645399","https://openalex.org/W2963186804","https://openalex.org/W2949622622","https://openalex.org/W2291175721","https://openalex.org/W1514989902","https://openalex.org/W2890056239","https://openalex.org/W3033249503","https://openalex.org/W2964346077","https://openalex.org/W2963402509","https://openalex.org/W2964049641","https://openalex.org/W3026715030","https://openalex.org/W2946056067","https://openalex.org/W2148069367","https://openalex.org/W3202996579","https://openalex.org/W209789590","https://openalex.org/W2173316741","https://openalex.org/W3136756258","https://openalex.org/W3194891820","https://openalex.org/W2982168727","https://openalex.org/W3103882218"],"abstract_inverted_index":{"Gaussian":[0],"process":[1],"(GP)":[2],"regression":[3],"with":[4,127],"1D":[5],"inputs":[6],"can":[7,32,40,47,121],"often":[8],"be":[9,41,48,122],"performed":[10],"in":[11,116],"linear":[12],"time":[13,125],"via":[14,77],"a":[15,56],"stochastic":[16],"differential":[17],"equation":[18],"formulation.":[19],"However,":[20],"for":[21,99],"non-Gaussian":[22],"likelihoods,":[23],"this":[24,52],"requires":[25],"application":[26],"of":[27,129],"approximate":[28],"inference":[29,46,76,115],"methods":[30],"which":[31,93],"make":[33],"the":[34],"implementation":[35,92],"difficult,":[36],"e.g.,":[37],"expectation":[38],"propagation":[39],"numerically":[42],"unstable":[43],"and":[44,84,97,112],"variational":[45,70,114],"computationally":[49],"inefficient.":[50],"In":[51],"paper,":[53],"we":[54],"propose":[55],"new":[57],"method":[58,67],"that":[59,120],"removes":[60],"such":[61],"difficulties.":[62],"Building":[63],"upon":[64],"an":[65,89],"existing":[66],"called":[68],"conjugate-computation":[69],"inference,":[71],"our":[72,107],"approach":[73,108],"enables":[74],"linear-time":[75],"Kalman":[78],"recursions":[79],"while":[80],"avoiding":[81],"numerical":[82],"instabilities":[83],"convergence":[85],"issues.":[86],"We":[87],"provide":[88],"efficient":[90],"JAX":[91],"exploits":[94],"just-in-time":[95],"compilation":[96],"allows":[98],"fast":[100,111],"automatic":[101],"differentiation":[102],"through":[103],"large":[104],"for-loops.":[105],"Overall,":[106],"leads":[109],"to":[110,124],"stable":[113],"state-space":[117],"GP":[118],"models":[119],"scaled":[123],"series":[126],"millions":[128],"data":[130],"points.":[131]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
