{"id":"https://openalex.org/W4283736709","doi":"https://doi.org/10.48550/arxiv.2206.12663","title":"Statistical inference with implicit SGD: proximal Robbins-Monro vs. Polyak-Ruppert","display_name":"Statistical inference with implicit SGD: proximal Robbins-Monro vs. Polyak-Ruppert","publication_year":2022,"publication_date":"2022-06-25","ids":{"openalex":"https://openalex.org/W4283736709","doi":"https://doi.org/10.48550/arxiv.2206.12663"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2206.12663","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2206.12663","pdf_url":"https://arxiv.org/pdf/2206.12663","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":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2206.12663","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065674806","display_name":"Yoonhyung Lee","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lee, Yoonhyung","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011683271","display_name":"Sungdong Lee","orcid":"https://orcid.org/0000-0003-0655-5050"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee, Sungdong","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5016994398","display_name":"Joong\u2010Ho Won","orcid":"https://orcid.org/0000-0002-5597-9557"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Won, Joong-Ho","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065674806"],"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/T10136","display_name":"Statistical Methods and Inference","score":0.9947999715805054,"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"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9947999715805054,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9889000058174133,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9854000210762024,"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/estimator","display_name":"Estimator","score":0.6826069951057434},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6391283273696899},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"Statistical inference","score":0.551701545715332},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5258715152740479},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5244778990745544},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.47626325488090515},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4479856789112091},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.32855910062789917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28875669836997986},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2539947032928467},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1584930717945099},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11644908785820007}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6826069951057434},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6391283273696899},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.551701545715332},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5258715152740479},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5244778990745544},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.47626325488090515},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4479856789112091},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32855910062789917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28875669836997986},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2539947032928467},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1584930717945099},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11644908785820007},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2206.12663","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2206.12663","pdf_url":"https://arxiv.org/pdf/2206.12663","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":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2206.12663","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2206.12663","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2206.12663","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2206.12663","pdf_url":"https://arxiv.org/pdf/2206.12663","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4287880334","https://openalex.org/W3103325625","https://openalex.org/W4366700029","https://openalex.org/W4285230481","https://openalex.org/W1486898455","https://openalex.org/W137830373","https://openalex.org/W3000984192","https://openalex.org/W2103073163","https://openalex.org/W4286952477","https://openalex.org/W4321348134"],"abstract_inverted_index":{"The":[0,95],"implicit":[1],"stochastic":[2],"gradient":[3],"descent":[4],"(ISGD),":[5],"a":[6,90],"proximal":[7,43,47],"version":[8],"of":[9,32,36,68,82,93,113,139],"SGD,":[10],"is":[11,111],"gaining":[12],"interest":[13],"in":[14,54,142],"the":[15,33,106,114,122,137,143],"literature":[16],"due":[17],"to":[18,100,135],"its":[19],"stability":[20],"over":[21],"(explicit)":[22],"SGD.":[23],"In":[24],"this":[25,140],"paper,":[26],"we":[27,61],"conduct":[28],"an":[29],"in-depth":[30],"analysis":[31,110],"two":[34],"modes":[35],"ISGD":[37,144],"for":[38,51,105],"smooth":[39],"convex":[40],"functions,":[41],"namely":[42],"Robbins-Monro":[44],"(proxRM)":[45],"and":[46,71,74,78,125],"Poylak-Ruppert":[48],"(proxPR)":[49],"procedures,":[50],"their":[52,75,83],"use":[53],"statistical":[55],"inference":[56],"on":[57],"model":[58,107,117],"parameters.":[59,108],"Specifically,":[60],"derive":[62],"non-asymptotic":[63],"point":[64],"estimation":[65],"error":[66],"bounds":[67],"both":[69],"proxRM":[70],"proxPR":[72],"iterates":[73],"limiting":[76],"distributions,":[77],"propose":[79],"on-line":[80,130],"estimators":[81,97,133],"asymptotic":[84],"covariance":[85,131],"matrices":[86],"that":[87,119],"require":[88],"only":[89],"single":[91],"run":[92],"ISGD.":[94],"latter":[96],"are":[98],"used":[99],"construct":[101],"valid":[102],"confidence":[103],"intervals":[104],"Our":[109,129],"free":[112],"generalized":[115],"linear":[116],"assumption":[118],"has":[120],"limited":[121],"preceding":[123],"analyses,":[124],"employs":[126],"feasible":[127],"procedures.":[128],"matrix":[132],"appear":[134],"be":[136],"first":[138],"kind":[141],"literature.":[145]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2022-07-01T00:00:00"}