{"id":"https://openalex.org/W2073715498","doi":"https://doi.org/10.1109/isic.2007.4450928","title":"Random Scaling of Quasi-Newton BFGS Method to Improve the O(N&lt;sup&gt;2&lt;/sup&gt;)-operation Approximation of Covariance-matrix Inverse in Gaussian Process","display_name":"Random Scaling of Quasi-Newton BFGS Method to Improve the O(N&lt;sup&gt;2&lt;/sup&gt;)-operation Approximation of Covariance-matrix Inverse in Gaussian Process","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2073715498","doi":"https://doi.org/10.1109/isic.2007.4450928","mag":"2073715498"},"language":"en","primary_location":{"id":"doi:10.1109/isic.2007.4450928","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isic.2007.4450928","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE 22nd International Symposium on Intelligent Control","raw_type":"proceedings-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/A5053064477","display_name":"Yunong Zhang","orcid":"https://orcid.org/0000-0002-2228-0395"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yunong Zhang","raw_affiliation_strings":["Department of Electronics and Communication Engineering, Sun Yat-Sen University, Guangzhou, China","Sun Yat-sen University, Guangzhou"],"affiliations":[{"raw_affiliation_string":"Department of Electronics and Communication Engineering, Sun Yat-Sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"Sun Yat-sen University, Guangzhou","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086446911","display_name":"Douglas J. Leith","orcid":"https://orcid.org/0000-0003-4056-4014"},"institutions":[{"id":"https://openalex.org/I181647926","display_name":"University of Strathclyde","ror":"https://ror.org/00n3w3b69","country_code":"GB","type":"education","lineage":["https://openalex.org/I181647926"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"W. E. Leithead","raw_affiliation_strings":["Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, UK","Electronic And Electrical Engineering"],"affiliations":[{"raw_affiliation_string":"Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, UK","institution_ids":["https://openalex.org/I181647926"]},{"raw_affiliation_string":"Electronic And Electrical Engineering","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086446911","display_name":"Douglas J. Leith","orcid":"https://orcid.org/0000-0003-4056-4014"},"institutions":[{"id":"https://openalex.org/I181231927","display_name":"National University of Ireland","ror":"https://ror.org/00shsf120","country_code":"IE","type":"education","lineage":["https://openalex.org/I181231927"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"D. J. Leith","raw_affiliation_strings":["Hamilton Institute, National University of Ireland, Kildare, Ireland","Electronic And Electrical Engineering"],"affiliations":[{"raw_affiliation_string":"Hamilton Institute, National University of Ireland, Kildare, Ireland","institution_ids":["https://openalex.org/I181231927"]},{"raw_affiliation_string":"Electronic And Electrical Engineering","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053064477"],"corresponding_institution_ids":["https://openalex.org/I157773358"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.09571004,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"452","last_page":"457"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9962999820709229,"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":0.9962999820709229,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9855999946594238,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9840999841690063,"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/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.6329105496406555},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6300207376480103},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.5958899259567261},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5057909488677979},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5001459121704102},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4982945919036865},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.4788379967212677},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47599780559539795},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.4740852117538452},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4294036626815796},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3460514545440674},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34237784147262573},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.31583404541015625},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.18458372354507446},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10079005360603333}],"concepts":[{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.6329105496406555},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6300207376480103},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.5958899259567261},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5057909488677979},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5001459121704102},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4982945919036865},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.4788379967212677},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47599780559539795},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.4740852117538452},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4294036626815796},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3460514545440674},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34237784147262573},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.31583404541015625},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.18458372354507446},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10079005360603333},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isic.2007.4450928","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isic.2007.4450928","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE 22nd International Symposium on Intelligent Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W175079832","https://openalex.org/W1484735710","https://openalex.org/W1618393386","https://openalex.org/W1996705509","https://openalex.org/W2014530379","https://openalex.org/W2053498134","https://openalex.org/W2069752241","https://openalex.org/W2077847045","https://openalex.org/W2101482846","https://openalex.org/W2130317597","https://openalex.org/W2133253631","https://openalex.org/W2138398260","https://openalex.org/W2158831443","https://openalex.org/W2163760546","https://openalex.org/W2165552175","https://openalex.org/W4253756272"],"related_works":["https://openalex.org/W3012383564","https://openalex.org/W2013605080","https://openalex.org/W2280670759","https://openalex.org/W3210693517","https://openalex.org/W4318192194","https://openalex.org/W2026245502","https://openalex.org/W3197176902","https://openalex.org/W4324358988","https://openalex.org/W4293559771","https://openalex.org/W2060767695"],"abstract_inverted_index":{"Gaussian":[0,20],"process":[1,21],"(GP)":[2],"is":[3,34,45],"a":[4,76,96],"Bayesian":[5],"nonparametric":[6],"regression":[7],"model,":[8],"showing":[9],"good":[10],"performance":[11],"in":[12,69,79],"various":[13],"applications.":[14],"Similar":[15],"to":[16,61,112],"other":[17,113],"computational":[18],"models,":[19],"frequently":[22],"encounters":[23],"the":[24,46,52,63,70,87,90],"matrix-inverse":[25,98],"problem":[26],"during":[27,75],"its":[28],"model-tuning":[29],"procedure.":[30],"The":[31],"matrix":[32,47,68],"inversion":[33],"generally":[35],"of":[36,66,94],"O(N":[37,53],"<sup":[38,54],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[39,55],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">3</sup>":[40],")":[41],"operations":[42],"where":[43],"N":[44],"dimension.":[48],"We":[49],"proposed":[50],"using":[51,86],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[56],")-operation":[57],"quasi-Newton":[58],"BFGS":[59,97,106],"method":[60],"approximate/replace":[62],"exact":[64],"inverse":[65],"covariance":[67],"GP":[71],"context.":[72],"As":[73],"inspired":[74],"paper":[77,81],"revision,":[78],"this":[80],"we":[82],"show":[83],"that":[84],"by":[85],"random-scaling":[88,105],"technique,":[89],"accuracy":[91],"and":[92],"effectiveness":[93],"such":[95],"approximation":[99],"could":[100,108],"be":[101,109],"further":[102],"improved.":[103],"These":[104],"techniques":[107],"widely":[110],"generalized":[111],"machine-learning":[114],"systems":[115],"which":[116],"rely":[117],"on":[118],"explicit":[119],"matrix-inverse.":[120]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
