{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T14:05:45Z","timestamp":1783087545387,"version":"3.54.6"},"reference-count":24,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T00:00:00Z","timestamp":1690416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"Hong Kong Research Grants Council"},{"DOI":"10.13039\/501100001839","name":"University Grants Committee","doi-asserted-by":"publisher","award":["14301821"],"award-info":[{"award-number":["14301821"]}],"id":[{"id":"10.13039\/501100001839","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001839","name":"University Grants Committee","doi-asserted-by":"publisher","award":["14306219"],"award-info":[{"award-number":["14306219"]}],"id":[{"id":"10.13039\/501100001839","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001839","name":"University Grants Committee","doi-asserted-by":"publisher","award":["14306620"],"award-info":[{"award-number":["14306620"]}],"id":[{"id":"10.13039\/501100001839","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Start-up Fund for New Recruits of The Hong Kong Polytechnic University","award":["P0044617"],"award-info":[{"award-number":["P0044617"]}]},{"name":"Start-up Fund for New Recruits of The Hong Kong Polytechnic University","award":["P0042888"],"award-info":[{"award-number":["P0042888"]}]},{"name":"Start-up Fund for New Recruits of The Hong Kong Polytechnic University","award":["A0045417"],"award-info":[{"award-number":["A0045417"]}]},{"name":"Start-up Fund for New Recruits of The Hong Kong Polytechnic University","award":["A0045931"],"award-info":[{"award-number":["A0045931"]}]},{"name":"Hong Kong Research Grants Council"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11961028"],"award-info":[{"award-number":["11961028"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Direct Grants for Research"},{"DOI":"10.13039\/501100004853","name":"Chinese University of Hong Kong","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004853","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004377","name":"The Hong Kong Polytechnic University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004377","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,2,12]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>We propose a debiased stochastic gradient descent algorithm for online statistical inference with high-dimensional data. Our approach combines the debiasing technique developed in high-dimensional statistics with the stochastic gradient descent algorithm. It can be used to construct confidence intervals efficiently in an online fashion. Our proposed algorithm has several appealing aspects: as a one-pass algorithm, it reduces the time complexity; in addition, each update step requires only the current data together with the previous estimate, which reduces the space complexity. We establish the asymptotic normality of the proposed estimator under mild conditions on the sparsity level of the parameter and the data distribution. Numerical experiments demonstrate that the proposed debiased stochastic gradient descent algorithm attains nominal coverage probability. Furthermore, we illustrate our method with analysis of a high-dimensional text dataset.<\/jats:p>","DOI":"10.1093\/biomet\/asad046","type":"journal-article","created":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T15:12:28Z","timestamp":1690470748000},"page":"93-108","source":"Crossref","is-referenced-by-count":18,"title":["Online inference with debiased stochastic gradient descent"],"prefix":"10.1093","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9225-2218","authenticated-orcid":false,"given":"Ruijian","family":"Han","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, The Hong Kong Polytechnic University , 11 Yuk Choi Road, Hung Hom , Kowloon 999077, Hong Kong SAR"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7901-2148","authenticated-orcid":false,"given":"Lan","family":"Luo","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Epidemiology, Rutgers School of Public Health , 683 Hoes Lane West , Piscataway, New Jersey 08854, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1293-1040","authenticated-orcid":false,"given":"Yuanyuan","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Chinese University of Hong Kong , Central Avenue , Shatin, New Territories 999077, Hong Kong SAR"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5218-9269","authenticated-orcid":false,"given":"Jian","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, The Hong Kong Polytechnic University , 11 Yuk Choi Road, Hung Hom , Kowloon 999077, Hong Kong SAR"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,7,27]]},"reference":[{"key":"2024021219285091700_asad046-B1","first-page":"1538","volume-title":"Proc. 25th Int. Conf. Neural Information Processing Systems (NIPS\u201912), vol","author":"Agarwal","year":"2012"},{"key":"2024021219285091700_asad046-B2","first-page":"30","volume-title":"Proc. Workshop on Language in Social Media (LSM 2011).","author":"Agarwal","year":"2011"},{"key":"2024021219285091700_asad046-B3","volume-title":"Theory and Applications","author":"B\u00fchlmann","year":"2011"},{"key":"2024021219285091700_asad046-B4","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1214\/18-AOS1801","article-title":"Statistical inference for model parameters in stochastic gradient descent","volume":"48","author":"Chen","year":"2020","journal-title":"Ann. Statist."},{"key":"2024021219285091700_asad046-B5","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1080\/01621459.2021.1979011","article-title":"Online debiasing for adaptively collected high-dimensional data with applications to time series analysis","volume":"118","author":"Deshpande","year":"2023","journal-title":"J. Am. Statist. Assoc"},{"key":"2024021219285091700_asad046-B6","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1109\/18.382009","article-title":"De-noising by soft-thresholding","volume":"41","author":"Donoho","year":"1995","journal-title":"IEEE Trans. Info. Theory"},{"key":"2024021219285091700_asad046-B7","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1111\/sjos.12378","article-title":"Scalable statistical inference for averaged implicit stochastic gradient descent","volume":"46","author":"Fang","year":"2019","journal-title":"Scand. J. Statist"},{"key":"2024021219285091700_asad046-B8","doi-asserted-by":"crossref","first-page":"2061","DOI":"10.1137\/110848876","article-title":"Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization, II: Shrinking procedures and optimal algorithms","volume":"23","author":"Ghadimi","year":"2013","journal-title":"SIAM J. Optimiz"},{"key":"2024021219285091700_asad046-B9","author":"Han","year":"2021"},{"key":"2024021219285091700_asad046-B10","first-page":"2869","article-title":"Confidence intervals and hypothesis testing for high-dimensional regression","volume":"15","author":"Javanmard","year":"2014","journal-title":"J. Mach. Learn. Res"},{"key":"2024021219285091700_asad046-B11","first-page":"272","volume-title":"Proc. Human Language Technologies: 2009 Ann. Conf. North American Chapter of the Association for Computational Linguistics","author":"Kogan","year":"2009"},{"key":"2024021219285091700_asad046-B12","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1111\/rssb.12352","article-title":"Renewable estimation and incremental inference in generalized linear models with streaming data sets","volume":"82","author":"Luo","year":"2020","journal-title":"J. R. Statist. Soc. B"},{"key":"2024021219285091700_asad046-B13","doi-asserted-by":"crossref","first-page":"2029","DOI":"10.1080\/01621459.2022.2026778","article-title":"Real-time regression analysis of streaming clustered data with possible abnormal data batches","volume":"118","author":"Luo","year":"2023","journal-title":"J. Am. Statist. Assoc"},{"key":"2024021219285091700_asad046-B14","first-page":"681","volume-title":"Proc. 26th Ann. Int. Conf. Machine Learning (ICML\u201909).","author":"Ma","year":"2009"},{"key":"2024021219285091700_asad046-B15","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1137\/0330046","article-title":"Acceleration of stochastic approximation by averaging","volume":"30","author":"Polyak","year":"1992","journal-title":"SIAM J. Contr. Optimiz"},{"key":"2024021219285091700_asad046-B16","volume-title":"R: A Language and Environment for Statistical Computing","author":"R Development Core Team","year":"2024"},{"key":"2024021219285091700_asad046-B17","author":"Ruppert","year":"1988"},{"key":"2024021219285091700_asad046-B18","first-page":"1865","article-title":"Stochastic methods for \u21131-regularized loss minimization","volume":"12","author":"Shalev-Shwartz","year":"2011","journal-title":"J. Mach. Learn. Res"},{"key":"2024021219285091700_asad046-B19","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1080\/01621459.2019.1710154","article-title":"Statistical inference for high-dimensional models via recursive online-score estimation","volume":"116","author":"Shi","year":"2021","journal-title":"J. Am. Statist. Assoc"},{"key":"2024021219285091700_asad046-B20","doi-asserted-by":"crossref","first-page":"1694","DOI":"10.1214\/16-AOS1506","article-title":"Asymptotic and finite-sample properties of estimators based on stochastic gradients","volume":"45","author":"Toulis","year":"2017","journal-title":"Ann. Statist."},{"key":"2024021219285091700_asad046-B21","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1214\/14-AOS1221","article-title":"On asymptotically optimal confidence regions and tests for high-dimensional models","volume":"42","author":"van de Geer","year":"2014","journal-title":"Ann. Statist."},{"key":"2024021219285091700_asad046-B22","first-page":"2116","volume-title":"Proc. 22nd Int. Conf. Neural Information Processing Systems (NIPS\u201909).","author":"Xiao","year":"2009"},{"key":"2024021219285091700_asad046-B23","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1111\/rssb.12026","article-title":"Confidence intervals for low dimensional parameters in high dimensional linear models","volume":"76","author":"Zhang","year":"2014","journal-title":"J. R. Statist. Soc. B"},{"key":"2024021219285091700_asad046-B24","first-page":"2541","article-title":"On model selection consistency of lasso","volume":"7","author":"Zhao","year":"2006","journal-title":"J. Mach. Learn. Res"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asad046\/51761768\/asad046.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/111\/1\/93\/56665697\/asad046.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/111\/1\/93\/56665697\/asad046.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,12]],"date-time":"2024-02-12T19:29:42Z","timestamp":1707766182000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/111\/1\/93\/7232226"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,27]]},"references-count":24,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,7,27]]},"published-print":{"date-parts":[[2024,2,12]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asad046","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,3,1]]},"published":{"date-parts":[[2023,7,27]]}}}