{"id":"https://openalex.org/W7111044701","doi":"https://doi.org/10.48550/arxiv.2512.06143","title":"gp2Scale: A Class of Compactly-Supported Non-Stationary Kernels and Distributed Computing for Exact Gaussian Processes on 10 Million Data Points","display_name":"gp2Scale: A Class of Compactly-Supported Non-Stationary Kernels and Distributed Computing for Exact Gaussian Processes on 10 Million Data Points","publication_year":2025,"publication_date":"2025-12-05","ids":{"openalex":"https://openalex.org/W7111044701","doi":"https://doi.org/10.48550/arxiv.2512.06143"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2512.06143","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.06143","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2512.06143","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Noack, Marcus M.","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Noack, Marcus M.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Risser, Mark D.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Risser, Mark D.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Luo, Hengrui","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luo, Hengrui","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Tekriwal, Vardaan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tekriwal, Vardaan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Pandolfi, Ronald J.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pandolfi, Ronald J.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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":0.8950999975204468,"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":0.8950999975204468,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.05090000107884407,"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"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.014299999922513962,"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/kernel","display_name":"Kernel (algebra)","score":0.691100001335144},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.6281999945640564},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5543000102043152},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5023000240325928},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4765999913215637},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4309999942779541},{"id":"https://openalex.org/keywords/exploit","display_name":"Exploit","score":0.41260001063346863},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.3919999897480011},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.385699987411499}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.691100001335144},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.6281999945640564},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.576200008392334},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5543000102043152},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5023000240325928},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48399999737739563},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4765999913215637},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4309999942779541},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.41260001063346863},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4065000116825104},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3919999897480011},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.385699987411499},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.3479999899864197},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.34630000591278076},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3287999927997589},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3278999924659729},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.3061000108718872},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.3005000054836273},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.2624000012874603}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2512.06143","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.06143","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2512.06143","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.06143","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Despite":[0],"a":[1,12,57,73,107],"large":[2],"corpus":[3],"of":[4,32,38,47,106,123,139,198],"recent":[5],"work":[6],"on":[7,64,92,154],"scaling":[8],"up":[9],"Gaussian":[10,81,207],"processes,":[11],"stubborn":[13],"trade-off":[14],"between":[15],"computational":[16],"speed,":[17],"prediction":[18],"and":[19,23,43,49,100,116,144,158,191,195],"uncertainty":[20],"quantification":[21],"accuracy,":[22],"customizability":[24],"persists.":[25],"This":[26],"is":[27,133],"because":[28],"the":[29,45,65,103,121,129,137,140,145,174,196],"vast":[30],"majority":[31],"existing":[33,104],"methodologies":[34],"exploit":[35],"various":[36],"levels":[37],"approximations":[39],"that":[40,78],"lower":[41],"accuracy":[42],"limit":[44],"flexibility":[46],"kernel":[48,95,110,188],"noise-model":[50],"designs":[51],"--":[52,186,194],"an":[53],"unacceptable":[54],"drawback":[55],"at":[56],"time":[58],"when":[59],"expressive":[60],"non-stationary":[61,117],"kernels":[62,118],"are":[63],"rise":[66],"in":[67,128,171,179],"many":[68,172],"fields.":[69],"Here,":[70],"we":[71,75,166],"propose":[72],"methodology":[74],"term":[76],"\\emph{gp2Scale}":[77],"scales":[79],"exact":[80],"processes":[82],"to":[83,120],"more":[84],"than":[85],"10":[86],"million":[87],"data":[88],"points":[89],"without":[90],"relying":[91],"inducing":[93],"points,":[94],"interpolation,":[96],"or":[97],"neighborhood-based":[98],"approximations,":[99],"instead":[101],"leveraging":[102],"capabilities":[105],"GP:":[108],"its":[109,180],"design.":[111],"Highly":[112],"flexible,":[113],"compactly":[114],"supported,":[115],"lead":[119],"identification":[122],"naturally":[124],"occurring":[125],"sparse":[126],"structure":[127],"covariance":[130],"matrix,":[131],"which":[132],"then":[134],"exploited":[135],"for":[136,147,205],"calculations":[138],"linear":[141],"system":[142],"solution":[143],"log-determinant":[146],"training.":[148],"We":[149],"demonstrate":[150],"our":[151],"method's":[152,175],"functionality":[153],"several":[155],"real-world":[156],"datasets":[157],"compare":[159],"it":[160,202],"with":[161],"state-of-the-art":[162],"approximation":[163,169],"algorithms.":[164],"Although":[165],"show":[167],"superior":[168],"performance":[170],"cases,":[173],"real":[176],"power":[177],"lies":[178],"agnosticism":[181],"toward":[182],"arbitrary":[183],"GP":[184],"customizations":[185],"core":[187],"design,":[189],"noise,":[190],"mean":[192],"functions":[193],"type":[197],"input":[199],"space,":[200],"making":[201],"optimally":[203],"suited":[204],"modern":[206],"process":[208],"applications.":[209]},"counts_by_year":[],"updated_date":"2025-12-10T02:49:46.989445","created_date":"2025-12-10T00:00:00"}