{"id":"https://openalex.org/W1980875804","doi":"https://doi.org/10.1137/14096311x","title":"Assessing Stochastic Algorithms for Large Scale Nonlinear Least Squares Problems Using Extremal Probabilities of Linear Combinations of Gamma Random Variables","display_name":"Assessing Stochastic Algorithms for Large Scale Nonlinear Least Squares Problems Using Extremal Probabilities of Linear Combinations of Gamma Random Variables","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1980875804","doi":"https://doi.org/10.1137/14096311x","mag":"1980875804"},"language":"en","primary_location":{"id":"doi:10.1137/14096311x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14096311x","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1404.0122","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Farbod Roosta-Khorasani","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Farbod Roosta-Khorasani","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"G\u00e1bor J. Sz\u00e9kely","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G\u00e1bor J. Sz\u00e9kely","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Uri M. Ascher","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Uri M. Ascher","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2331,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.90272456,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"3","issue":"1","first_page":"61","last_page":"90"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.5685999989509583,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.5685999989509583,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.08839999884366989,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.07500000298023224,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5331000089645386},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5171999931335449},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.5088000297546387},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.49050000309944153},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4731000065803528},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.44909998774528503},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4221000075340271},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.39590001106262207},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.3799999952316284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7748000025749207},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5331000089645386},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5171999931335449},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.5088000297546387},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.49050000309944153},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4799000024795532},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4731000065803528},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.44909998774528503},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4242999851703644},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4221000075340271},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39980000257492065},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.39590001106262207},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.37229999899864197},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3562000095844269},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.35510000586509705},{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.35249999165534973},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3253999948501587},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C24404364","wikidata":"https://www.wikidata.org/wiki/Q7246846","display_name":"Probabilistic analysis of algorithms","level":3,"score":0.30469998717308044},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.28870001435279846},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.28850001096725464},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.2667999863624573}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/14096311x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14096311x","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1404.0122","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.0122","pdf_url":"https://arxiv.org/pdf/1404.0122","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1404.0122","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.0122","pdf_url":"https://arxiv.org/pdf/1404.0122","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1964940941","https://openalex.org/W1968097571","https://openalex.org/W1978429862","https://openalex.org/W1991595986","https://openalex.org/W2005681075","https://openalex.org/W2007755560","https://openalex.org/W2013344542","https://openalex.org/W2019178284","https://openalex.org/W2033106066","https://openalex.org/W2046489591","https://openalex.org/W2051308685","https://openalex.org/W2052078443","https://openalex.org/W2052816682","https://openalex.org/W2057450058","https://openalex.org/W2057592393","https://openalex.org/W2061823996","https://openalex.org/W2063115808","https://openalex.org/W2104920672","https://openalex.org/W2131362196","https://openalex.org/W2131742412","https://openalex.org/W2150377124","https://openalex.org/W2161169693"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"stochastic":[3,38,43,114],"algorithms":[4],"for":[5],"efficiently":[6],"solving":[7],"a":[8,28],"class":[9],"of":[10,27,62,65,130,138,141,159,168,171],"large":[11],"scale":[12],"nonlinear":[13],"least":[14],"squares":[15],"(NLS)":[16],"problems":[17],"which":[18,163],"frequently":[19],"arise":[20],"in":[21,35,112,120],"applications.":[22],"We":[23,95,146],"propose":[24],"eight":[25],"variants":[26],"practical":[29],"randomized":[30,122],"algorithm":[31,115],"where":[32],"the":[33,36,47,60,63,72,82,91,118,153,169],"uncertainties":[34],"major":[37],"steps":[39,44],"are":[40,100,109,128],"quantified.":[41],"Such":[42],"involve":[45],"approximating":[46],"NLS":[48],"objective":[49],"function":[50],"using":[51],"Monte":[52],"Carlo":[53],"methods,":[54],"and":[55,78,103,148,155],"this":[56,172],"is":[57],"equivalent":[58],"to":[59,87,89,116],"estimation":[61],"trace":[64],"corresponding":[66],"symmetric":[67],"positive":[68],"semidefinite":[69],"matrices.":[70],"For":[71],"latter,":[73],"we":[74,126],"prove":[75,149],"tight":[76],"necessary":[77],"\\sufficient":[79],"conditions":[80,99],"on":[81],"sample":[83,106],"size":[84],"(which":[85],"translates":[86],"cost)":[88],"satisfy":[90],"prescribed":[92],"probabilistic":[93],"accuracy.":[94],"show":[96],"that":[97],"these":[98],"practically":[101],"computable":[102],"yield":[104],"small":[105],"sizes.":[107],"They":[108],"then":[110],"incorporated":[111],"our":[113],"quantify":[117],"uncertainty":[119],"each":[121],"step.":[123],"The":[124],"bounds":[125],"use":[127],"applications":[129],"more":[131],"general":[132],"results":[133,151],"regarding":[134],"extremal":[135],"tail":[136,157],"probabilities":[137,158],"linear":[139,161],"combinations":[140],"gamma":[142],"distributed":[143],"random":[144],"variables.":[145],"derive":[147],"new":[150],"concerning":[152],"maximal":[154],"minimal":[156],"such":[160],"combinations,":[162],"can":[164],"be":[165],"considered":[166],"independently":[167],"rest":[170],"paper.":[173]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}