{"id":"https://openalex.org/W2963970272","doi":"https://doi.org/10.1109/icassp.2016.7472090","title":"On projected stochastic gradient descent algorithm with weighted averaging for least squares regression","display_name":"On projected stochastic gradient descent algorithm with weighted averaging for least squares regression","publication_year":2016,"publication_date":"2016-03-01","ids":{"openalex":"https://openalex.org/W2963970272","doi":"https://doi.org/10.1109/icassp.2016.7472090","mag":"2963970272"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2016.7472090","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2016.7472090","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","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/A5066085947","display_name":"Kobi Cohen","orcid":"https://orcid.org/0000-0003-0532-009X"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Kobi Cohen","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110629459","display_name":"Angelia Nedi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Angelia Nedic","raw_affiliation_strings":["Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, IL"],"affiliations":[{"raw_affiliation_string":"Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, IL","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078518595","display_name":"R. Srikant","orcid":"https://orcid.org/0000-0003-1483-5204"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Srikant","raw_affiliation_strings":["Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, IL"],"affiliations":[{"raw_affiliation_string":"Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, IL","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066085947"],"corresponding_institution_ids":["https://openalex.org/I124227911"],"apc_list":null,"apc_paid":null,"fwci":0.9119,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75851056,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"239","issue":null,"first_page":"2314","last_page":"2318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998999834060669,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9966999888420105,"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/mathematics","display_name":"Mathematics","score":0.7331416606903076},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.6944526433944702},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6752743721008301},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5985324382781982},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5842151045799255},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5671712160110474},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5333661437034607},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.44720447063446045},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4409586787223816},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40978485345840454},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2397148609161377},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13542714715003967},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12636783719062805},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.08504527807235718}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7331416606903076},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.6944526433944702},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6752743721008301},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5985324382781982},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5842151045799255},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5671712160110474},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5333661437034607},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.44720447063446045},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4409586787223816},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40978485345840454},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2397148609161377},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13542714715003967},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12636783719062805},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.08504527807235718},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icassp.2016.7472090","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2016.7472090","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W92732855","https://openalex.org/W1568668329","https://openalex.org/W1957482736","https://openalex.org/W1992208280","https://openalex.org/W1998880679","https://openalex.org/W2024484010","https://openalex.org/W2045744861","https://openalex.org/W2061863621","https://openalex.org/W2063746322","https://openalex.org/W2086161653","https://openalex.org/W2096199223","https://openalex.org/W2100556411","https://openalex.org/W2103971893","https://openalex.org/W2105591650","https://openalex.org/W2105875671","https://openalex.org/W2107438106","https://openalex.org/W2112269233","https://openalex.org/W2118545728","https://openalex.org/W2124541940","https://openalex.org/W2132211083","https://openalex.org/W2138507770","https://openalex.org/W2151695970","https://openalex.org/W2157187092","https://openalex.org/W2159930037","https://openalex.org/W2169713291","https://openalex.org/W2615070957","https://openalex.org/W2622597896","https://openalex.org/W2936995161","https://openalex.org/W2963646202","https://openalex.org/W3100353959","https://openalex.org/W3141595720","https://openalex.org/W4297685995","https://openalex.org/W6640782186","https://openalex.org/W6674593956","https://openalex.org/W6675761068","https://openalex.org/W6676105031","https://openalex.org/W6676963778","https://openalex.org/W6683798259","https://openalex.org/W6711626769","https://openalex.org/W6761030284"],"related_works":["https://openalex.org/W4385609682","https://openalex.org/W2807251790","https://openalex.org/W4234593354","https://openalex.org/W2981302852","https://openalex.org/W3002546633","https://openalex.org/W2964170259","https://openalex.org/W2378346679","https://openalex.org/W2765682467","https://openalex.org/W4206119629","https://openalex.org/W4382937879"],"abstract_inverted_index":{"The":[0],"problem":[1],"of":[2,6,45,80,124,137,171,183],"least":[3],"squares":[4],"regression":[5],"a":[7,24,41],"d-dimensional":[8],"unknown":[9,47],"parameter":[10,176],"is":[11,30,36],"considered.":[12],"A":[13],"stochastic":[14],"gradient":[15],"descent":[16],"based":[17],"algorithm":[18,185],"with":[19,95,105,193],"weighted":[20],"iterate-averaging":[21],"that":[22,86,143,164],"uses":[23],"single":[25],"pass":[26],"over":[27],"the":[28,46,62,67,71,75,78,81,87,91,100,116,121,125,129,135,159,169,184],"data":[29],"studied":[31],"and":[32,77,93,128,174,191],"its":[33],"convergence":[34,63,122],"rate":[35,96,106,123],"analyzed.":[37],"We":[38,84,113,141,156],"first":[39],"consider":[40],"bounded":[42],"constraint":[43,82,101],"set":[44,102],"parameter.":[48],"Under":[49],"some":[50,148],"standard":[51],"regularity":[52],"assumptions,":[53],"we":[54],"provide":[55],"an":[56],"explicit":[57],"O(1/k)":[58],"upper":[59,160],"bound":[60,161],"on":[61,66],"rate,":[64],"depending":[65],"variance":[68,88],"(due":[69],"to":[70,188],"additive":[72],"noise":[73],"in":[74,201],"measurements)":[76],"size":[79],"set.":[83,177],"show":[85,142],"term":[89,103],"dominates":[90],"error":[92],"decreases":[94,104],"1":[97],"/k,":[98],"while":[99],"log":[107],"k/k":[108],"<sup":[109],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[110],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[111],".":[112],"then":[114],"compare":[115],"asymptotic":[117],"ratio":[118],"\u03c1":[119,144,165,194],"between":[120],"proposed":[126],"scheme":[127],"empirical":[130],"risk":[131],"minimizer":[132],"(ERM)":[133],"as":[134,186],"number":[136],"iterations":[138],"approaches":[139],"infinity.":[140],"\u2264":[145,166,195],"4":[146],"under":[147],"mild":[149],"conditions":[150],"for":[151,168,198],"all":[152],"d":[153,172,200],"\u2265":[154],"1.":[155],"further":[157],"improve":[158],"by":[162],"showing":[163],"4/3":[167,196],"case":[170],"=1":[173],"unbounded":[175],"Simulation":[178],"results":[179],"demonstrate":[180],"strong":[181],"performance":[182],"compared":[187],"existing":[189],"methods,":[190],"coincide":[192],"even":[197],"large":[199],"practice.":[202]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}