{"id":"https://openalex.org/W2568875900","doi":"https://doi.org/10.1137/16m1105396","title":"Faster Kernel Ridge Regression Using Sketching and Preconditioning","display_name":"Faster Kernel Ridge Regression Using Sketching and Preconditioning","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2568875900","doi":"https://doi.org/10.1137/16m1105396","mag":"2568875900"},"language":"en","primary_location":{"id":"doi:10.1137/16m1105396","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1105396","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072151198","display_name":"Haim Avron","orcid":"https://orcid.org/0000-0002-1688-9030"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Haim Avron","raw_affiliation_strings":["Aviv University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aviv University","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047290568","display_name":"Kenneth L. Clarkson","orcid":null},"institutions":[{"id":"https://openalex.org/I4210085935","display_name":"IBM Research - Almaden","ror":"https://ror.org/005w8dd04","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210085935","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kenneth L. Clarkson","raw_affiliation_strings":["IBM Almaden Research Center"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Almaden Research Center","institution_ids":["https://openalex.org/I4210085935"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102861589","display_name":"David P. Woodruff","orcid":"https://orcid.org/0000-0002-2158-1380"},"institutions":[{"id":"https://openalex.org/I4210085935","display_name":"IBM Research - Almaden","ror":"https://ror.org/005w8dd04","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210085935","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David P. Woodruff","raw_affiliation_strings":["IBM Almaden Research Center"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Almaden Research Center","institution_ids":["https://openalex.org/I4210085935"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.4232,"has_fulltext":false,"cited_by_count":99,"citation_normalized_percentile":{"value":0.99196082,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"38","issue":"4","first_page":"1116","last_page":"1138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9898999929428101,"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/T11609","display_name":"Geophysical Methods and Applications","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/kernel","display_name":"Kernel (algebra)","score":0.722819447517395},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.712910532951355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6412080526351929},{"id":"https://openalex.org/keywords/kernel-regression","display_name":"Kernel regression","score":0.5734096765518188},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.5289618372917175},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.47047004103660583},{"id":"https://openalex.org/keywords/ridge","display_name":"Ridge","score":0.45589756965637207},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45493942499160767},{"id":"https://openalex.org/keywords/polynomial-kernel","display_name":"Polynomial kernel","score":0.42195698618888855},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4215913712978363},{"id":"https://openalex.org/keywords/nonparametric-regression","display_name":"Nonparametric regression","score":0.41495025157928467},{"id":"https://openalex.org/keywords/variable-kernel-density-estimation","display_name":"Variable kernel density estimation","score":0.4105919599533081},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37450718879699707},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3643577992916107},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.36138367652893066},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33179599046707153},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3239327073097229},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.22740483283996582},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.2065129280090332},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19200041890144348},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09137669205665588},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.084259033203125}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.722819447517395},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.712910532951355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6412080526351929},{"id":"https://openalex.org/C200695384","wikidata":"https://www.wikidata.org/wiki/Q1739319","display_name":"Kernel regression","level":3,"score":0.5734096765518188},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.5289618372917175},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.47047004103660583},{"id":"https://openalex.org/C32277403","wikidata":"https://www.wikidata.org/wiki/Q740445","display_name":"Ridge","level":2,"score":0.45589756965637207},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45493942499160767},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.42195698618888855},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4215913712978363},{"id":"https://openalex.org/C74127309","wikidata":"https://www.wikidata.org/wiki/Q3455886","display_name":"Nonparametric regression","level":3,"score":0.41495025157928467},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.4105919599533081},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37450718879699707},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3643577992916107},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.36138367652893066},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33179599046707153},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3239327073097229},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.22740483283996582},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.2065129280090332},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19200041890144348},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09137669205665588},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.084259033203125},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1105396","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1105396","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","display_name":"Climate action","score":0.5299999713897705}],"awards":[{"id":"https://openalex.org/G4297820378","display_name":null,"funder_award_id":"FA8750-12-C-0323","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G4713059963","display_name":null,"funder_award_id":"FA8750","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"}],"funders":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320332815","display_name":"Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1493892051","https://openalex.org/W1984720405","https://openalex.org/W2007399394","https://openalex.org/W2007500622","https://openalex.org/W2008776938","https://openalex.org/W2044514896","https://openalex.org/W2093529653","https://openalex.org/W2124659530","https://openalex.org/W2201600774","https://openalex.org/W2593960758","https://openalex.org/W2962768290","https://openalex.org/W2962937842","https://openalex.org/W3112410551","https://openalex.org/W3143835353"],"related_works":["https://openalex.org/W122742822","https://openalex.org/W2384322977","https://openalex.org/W2165576085","https://openalex.org/W2393746448","https://openalex.org/W4311138679","https://openalex.org/W1985324234","https://openalex.org/W2382911382","https://openalex.org/W4235184103","https://openalex.org/W4297632110","https://openalex.org/W2261298172"],"abstract_inverted_index":{"Kernel":[0],"ridge":[1,103],"regression":[2,11],"is":[3,22,71,165,180],"a":[4,17,57,87,159],"simple":[5],"yet":[6],"powerful":[7,88],"technique":[8,59,89],"for":[9,49,60,90,183],"nonparametric":[10],"whose":[12],"computation":[13],"amounts":[14],"to":[15,107,117,137,167,187],"solving":[16,127],"linear":[18,67],"system.":[19,68],"This":[20],"system":[21,130],"usually":[23],"dense":[24],"and":[25,93,177],"highly":[26,181],"ill-conditioned.":[27],"In":[28,52],"addition,":[29],"the":[30,33,36,39,62,65,95,118,128,132],"dimensions":[31],"of":[32,41,64,97,134,162,185],"matrix":[34],"are":[35,47],"same":[37],"as":[38,78,86,101],"number":[40,133,161],"data":[42],"points,":[43],"so":[44,121],"direct":[45],"methods":[46],"unrealistic":[48],"large-scale":[50],"datasets.":[51],"this":[53],"paper,":[54],"we":[55],"propose":[56],"preconditioning":[58],"accelerating":[61],"solution":[63],"aforementioned":[66],"The":[69],"preconditioner":[70],"based":[72],"on":[73],"random":[74,79,110,135,144,163],"feature":[75,111,145],"maps,":[76],"such":[77,100],"Fourier":[80],"features,":[81],"which":[82],"have":[83],"recently":[84],"emerged":[85],"speeding":[91],"up":[92,186],"scaling":[94],"training":[96,190],"kernel-based":[98],"methods,":[99],"kernel":[102,119],"regression,":[104],"by":[105,125],"resorting":[106],"approximations.":[108],"However,":[109],"maps":[112,146],"only":[113],"provide":[114],"crude":[115],"approximations":[116],"function,":[120],"delivering":[122],"state-of-the-art":[123],"results":[124],"directly":[126],"approximated":[129],"requires":[131],"features":[136,164],"be":[138,148],"very":[139],"large.":[140],"We":[141,172],"show":[142,178],"that":[143],"can":[147],"much":[149],"more":[150],"effective":[151,170,182],"in":[152],"forming":[153],"preconditioners,":[154],"since":[155],"under":[156],"certain":[157],"conditions":[158],"not-too-large":[160],"sufficient":[166],"yield":[168],"an":[169],"preconditioner.":[171],"empirically":[173],"evaluate":[174],"our":[175],"method":[176],"it":[179],"datasets":[184],"one":[188],"million":[189],"examples.":[191]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
