{"id":"https://openalex.org/W3004346979","doi":"https://doi.org/10.1109/wsc52266.2021.9715437","title":"On Constructing Confidence Region for Model Parameters in Stochastic Gradient Descent Via Batch Means","display_name":"On Constructing Confidence Region for Model Parameters in Stochastic Gradient Descent Via Batch Means","publication_year":2021,"publication_date":"2021-12-12","ids":{"openalex":"https://openalex.org/W3004346979","doi":"https://doi.org/10.1109/wsc52266.2021.9715437","mag":"3004346979"},"language":"en","primary_location":{"id":"doi:10.1109/wsc52266.2021.9715437","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wsc52266.2021.9715437","pdf_url":null,"source":{"id":"https://openalex.org/S4363607949","display_name":"2021 Winter Simulation Conference (WSC)","issn_l":null,"issn":null,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 Winter Simulation Conference (WSC)","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/A5100434324","display_name":"Yi Zhu","orcid":"https://orcid.org/0000-0003-3000-3918"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yi Zhu","raw_affiliation_strings":["WeRide Corp,San Jose,CA,95134"],"affiliations":[{"raw_affiliation_string":"WeRide Corp,San Jose,CA,95134","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028323106","display_name":"Jing Dong","orcid":"https://orcid.org/0000-0001-6387-4088"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jing Dong","raw_affiliation_strings":["Graduate School of Business, Columbia University,New York,NY,USA,10027"],"affiliations":[{"raw_affiliation_string":"Graduate School of Business, Columbia University,New York,NY,USA,10027","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100434324"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.377,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.56131987,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":1.0,"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":1.0,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.6878104209899902},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6648831367492676},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5144239068031311},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5059482455253601},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.49339190125465393},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47817522287368774},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.47730839252471924},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4761236310005188},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.46505698561668396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45715683698654175},{"id":"https://openalex.org/keywords/law-of-the-iterated-logarithm","display_name":"Law of the iterated logarithm","score":0.4565446376800537},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.44643980264663696},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4179896116256714},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3987642228603363},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37993723154067993},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19846242666244507},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16124024987220764},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.09205150604248047},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.06816264986991882}],"concepts":[{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.6878104209899902},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6648831367492676},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5144239068031311},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5059482455253601},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.49339190125465393},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47817522287368774},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.47730839252471924},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4761236310005188},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.46505698561668396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45715683698654175},{"id":"https://openalex.org/C139907963","wikidata":"https://www.wikidata.org/wiki/Q198740","display_name":"Law of the iterated logarithm","level":3,"score":0.4565446376800537},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.44643980264663696},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4179896116256714},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3987642228603363},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37993723154067993},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19846242666244507},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16124024987220764},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.09205150604248047},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.06816264986991882},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/wsc52266.2021.9715437","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wsc52266.2021.9715437","pdf_url":null,"source":{"id":"https://openalex.org/S4363607949","display_name":"2021 Winter Simulation Conference (WSC)","issn_l":null,"issn":null,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 Winter Simulation Conference (WSC)","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":21,"referenced_works":["https://openalex.org/W1587317356","https://openalex.org/W1629501955","https://openalex.org/W1992208280","https://openalex.org/W1994616650","https://openalex.org/W2086161653","https://openalex.org/W2091825929","https://openalex.org/W2096840748","https://openalex.org/W2110335061","https://openalex.org/W2117434338","https://openalex.org/W2137594042","https://openalex.org/W2141422615","https://openalex.org/W2166630989","https://openalex.org/W2170771993","https://openalex.org/W2525518963","https://openalex.org/W2727996392","https://openalex.org/W2885329750","https://openalex.org/W2964121744","https://openalex.org/W3007705674","https://openalex.org/W3101606912","https://openalex.org/W4241575764","https://openalex.org/W6753616334"],"related_works":["https://openalex.org/W4206903459","https://openalex.org/W2754816816","https://openalex.org/W4366280654","https://openalex.org/W3160167280","https://openalex.org/W4362706668","https://openalex.org/W4231621013","https://openalex.org/W3171021120","https://openalex.org/W3008318776","https://openalex.org/W2041416246","https://openalex.org/W3020853991"],"abstract_inverted_index":{"We":[0,60],"study":[1],"an":[2],"easy-to-implement":[3],"algorithm":[4],"to":[5,22,31,67],"construct":[6],"asymptotically":[7],"valid":[8],"confidence":[9],"regions":[10],"for":[11,56],"model":[12],"parameters":[13],"in":[14],"stochastic":[15],"gradient":[16],"descent.":[17],"The":[18],"main":[19],"idea":[20],"is":[21,29],"cancel":[23],"out":[24],"the":[25,34,46,63],"covariance":[26],"matrix":[27],"which":[28],"hard/costly":[30],"estimate":[32],"using":[33],"batch":[35,64,71],"means":[36,65],"method":[37,66],"with":[38],"a":[39,50],"fixed":[40],"number":[41],"of":[42],"batches.":[43],"In":[44],"developing":[45],"algorithm,":[47],"we":[48],"establish":[49],"process-level":[51],"functional":[52],"central":[53],"limit":[54],"theorem":[55],"Polyak-Ruppert":[57],"averaging":[58],"iterates.":[59],"also":[61],"extend":[62],"accommodate":[68],"more":[69],"general":[70],"size":[72],"specifications.":[73]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}