{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T08:44:09Z","timestamp":1763369049022,"version":"3.45.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T00:00:00Z","timestamp":1759708800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T00:00:00Z","timestamp":1759708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7 para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/00013: Centro de Matem\u00e1tica da Universidade do Minho (CMAT\/UM)","UID\/00013: Centro de Matem\u00e1tica da Universidade do Minho (CMAT\/UM)"],"award-info":[{"award-number":["UID\/00013: Centro de Matem\u00e1tica da Universidade do Minho (CMAT\/UM)","UID\/00013: Centro de Matem\u00e1tica da Universidade do Minho (CMAT\/UM)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["2024.06508.BDANA","UIDB\/50014\/2020"],"award-info":[{"award-number":["2024.06508.BDANA","UIDB\/50014\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s00180-025-01673-8","type":"journal-article","created":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T07:44:46Z","timestamp":1759736686000},"page":"5769-5790","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Distributed Generalized Linear Models: A Privacy-Preserving Approach"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-5849-9971","authenticated-orcid":false,"given":"Daniel","family":"Tinoco","sequence":"first","affiliation":[]},{"given":"Raquel","family":"Menezes","sequence":"additional","affiliation":[]},{"given":"Carlos","family":"Baquero","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,6]]},"reference":[{"key":"1673_CR1","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/0024-3795(92)90379-O","volume":"162\u2013164","author":"E Anderson","year":"1992","unstructured":"Anderson E, Bai Z, Dongarra J (1992) Generalized qr factorization and its applications. Linear Algebra Appl 162\u2013164:243\u2013271. https:\/\/doi.org\/10.1016\/0024-3795(92)90379-O","journal-title":"Linear Algebra Appl"},{"key":"1673_CR2","doi-asserted-by":"publisher","DOI":"10.1201\/9781315171401","volume-title":"A computational approach to statistical learning","author":"T Arnold","year":"2019","unstructured":"Arnold T, Kane M, Lewis BW (2019) A computational approach to statistical learning. CRC Press, London"},{"key":"1673_CR3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971484","volume-title":"Numerical methods for least squares problems","author":"\u00c5 Bj\u00f6rck","year":"1996","unstructured":"Bj\u00f6rck \u00c5 (1996) Numerical methods for least squares problems. SIAM, Philadelphia"},{"issue":"336","key":"1673_CR4","doi-asserted-by":"publisher","first-page":"744","DOI":"10.2307\/2284221","volume":"66","author":"JM Chambers","year":"1971","unstructured":"Chambers JM (1971) Regression updating. J Am Stat Assoc 66(336):744\u2013748. https:\/\/doi.org\/10.2307\/2284221","journal-title":"J Am Stat Assoc"},{"key":"1673_CR5","doi-asserted-by":"publisher","first-page":"585","DOI":"10.4310\/SII.2013.v6.n4.a15","volume":"6","author":"C Chen","year":"2013","unstructured":"Chen C (2013) Distributed iteratively reweighted least squares and applications. Stat Its Interface 6:585\u2013593. https:\/\/doi.org\/10.4310\/SII.2013.v6.n4.a15","journal-title":"Stat Its Interface"},{"issue":"1","key":"1673_CR6","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1137\/080731992","volume":"34","author":"J Demmel","year":"2012","unstructured":"Demmel J, Grigori L, Hoemmen M, Langou J (2012) Communication-optimal parallel and sequential qr and lu factorizations. SIAM J Sci Comput 34(1):206\u2013239. https:\/\/doi.org\/10.1137\/080731992","journal-title":"SIAM J Sci Comput"},{"key":"1673_CR7","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1007\/11681878_14","volume-title":"Theory of cryptography","author":"C Dwork","year":"2006","unstructured":"Dwork C, McSherry F, Nissim K, Smith A (2006) Calibrating noise to sensitivity in private data analysis. In: Halevi S, Rabin T (eds) Theory of cryptography. Springer, Berlin, pp 265\u2013284"},{"key":"1673_CR8","doi-asserted-by":"publisher","unstructured":"Dwork C, Naor M, Pitassi T, Rothblum GN (2010) Differential privacy under continual observation. In: Proceedings of the Forty-Second ACM Symposium on Theory of Computing. STOC \u201910, pp. 715\u2013724. Association for Computing Machinery, New York, NY, USA. https:\/\/doi.org\/10.1145\/1806689.1806787","DOI":"10.1145\/1806689.1806787"},{"key":"1673_CR9","unstructured":"Elixir Core Team (2011) The Elixir Programming Language. https:\/\/elixir-lang.org\/"},{"key":"1673_CR10","unstructured":"Erlang\/OTP Core Team (1986) Erlang Programming Language. https:\/\/www.erlang.org\/"},{"key":"1673_CR11","doi-asserted-by":"publisher","first-page":"323","DOI":"10.2478\/popets-2021-0030","volume":"2","author":"D Froelicher","year":"2021","unstructured":"Froelicher D, Troncoso-Pastoriza JR, Pyrgelis A, Sav S, Sousa JS, Bossuat J-P, Hubaux J-P (2021) Scalable privacy-preserving distributed learning. Proc Privacy Enhanc Technol 2:323\u2013347","journal-title":"Proc Privacy Enhanc Technol"},{"issue":"3","key":"1673_CR12","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1093\/imamat\/12.3.329","volume":"12","author":"WM Gentleman","year":"1973","unstructured":"Gentleman WM (1973) Least squares computations by givens transformations without square roots. IMA J Appl Math 12(3):329\u2013336. https:\/\/doi.org\/10.1093\/imamat\/12.3.329","journal-title":"IMA J Appl Math"},{"issue":"3","key":"1673_CR13","doi-asserted-by":"publisher","first-page":"448","DOI":"10.2307\/2347147","volume":"23","author":"WM Gentleman","year":"1974","unstructured":"Gentleman WM (1974) Algorithm as 75: Basic procedures for large, sparse or weighted linear least problems. J Roy Stat Soc: Ser C (Appl Stat) 23(3):448\u2013454. https:\/\/doi.org\/10.2307\/2347147","journal-title":"J Roy Stat Soc: Ser C (Appl Stat)"},{"issue":"2","key":"1673_CR14","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1111\/j.2517-6161.1984.tb01288.x","volume":"46","author":"PJ Green","year":"1984","unstructured":"Green PJ (1984) Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives. J Roy Stat Soc: Ser B (Methodol) 46(2):149\u2013192","journal-title":"J Roy Stat Soc: Ser B (Methodol)"},{"key":"1673_CR15","unstructured":"Greene WH (2003) Econometric Analysis, 5th edn. Pearson Education, New York. http:\/\/pages.stern.nyu.edu\/%7Ewgreene\/Text\/econometricanalysis.htm"},{"issue":"4","key":"1673_CR16","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1515\/popets-2017-0053","volume":"2017","author":"A Gasc\u00f3n","year":"2017","unstructured":"Gasc\u00f3n A, Schoppmann P, Balle B, Raykova M, Doerner J, Zahur S, Evans D (2017) Privacy-Preserving Distributed Linear Regression on High-Dimensional Data. Proc Privacy Enhanc Technol 2017(4):345\u2013364. https:\/\/doi.org\/10.1515\/popets-2017-0053","journal-title":"Proc Privacy Enhanc Technol"},{"key":"1673_CR17","volume-title":"Matrix computations","author":"GH Golub","year":"1996","unstructured":"Golub GH, Loan CF (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, USA","edition":"3"},{"key":"1673_CR18","first-page":"669","volume":"27","author":"R Hall","year":"2011","unstructured":"Hall R, Fienberg SE, Nardi Y (2011) Secure multiple linear regression based on homomorphic encryption. J Off Stat 27:669\u2013691","journal-title":"J Off Stat"},{"key":"1673_CR19","doi-asserted-by":"publisher","first-page":"5122","DOI":"10.1109\/TIFS.2023.3301710","volume":"18","author":"A Hartebrodt","year":"2023","unstructured":"Hartebrodt A, R\u00f6ttger R (2023) Privacy of federated qr decomposition using additive secure multiparty computation. IEEE Trans Inf Forensics Secur 18:5122\u20135132. https:\/\/doi.org\/10.1109\/TIFS.2023.3301710","journal-title":"IEEE Trans Inf Forensics Secur"},{"key":"1673_CR20","doi-asserted-by":"publisher","unstructured":"IEEE (2019) Ieee standard for floating-point arithmetic. IEEE Std 754-2019 (Revision of IEEE 754-2008), 1\u201384 https:\/\/doi.org\/10.1109\/IEEESTD.2019.8766229","DOI":"10.1109\/IEEESTD.2019.8766229"},{"key":"1673_CR21","unstructured":"McMahan B, Moore E, Ramage D, Hampson S, Arcas BA (2017) Communication-efficient learning of deep networks from decentralized data. In: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, AISTATS. Proceedings of Machine Learning Research, vol. 54, pp. 1273\u20131282. PMLR, ???"},{"key":"1673_CR22","unstructured":"Murphy KP (2022) Probabilistic Machine Learning: An Introduction. MIT Press, London. http:\/\/probml.github.io\/book1"},{"issue":"3","key":"1673_CR23","doi-asserted-by":"publisher","first-page":"370","DOI":"10.2307\/2344614","volume":"135","author":"JA Nelder","year":"1972","unstructured":"Nelder JA, Wedderburn RWM (1972) Generalized linear models. J Roy Stat Soc Ser A (General) 135(3):370\u2013384","journal-title":"J Roy Stat Soc Ser A (General)"},{"key":"1673_CR24","doi-asserted-by":"publisher","unstructured":"Paige CC (1990) Some aspects of generalized QR factorizations. In: Reliable Numerical Commputation. Oxford University Press, Oxford. https:\/\/doi.org\/10.1093\/oso\/9780198535645.003.0006","DOI":"10.1093\/oso\/9780198535645.003.0006"},{"key":"1673_CR25","doi-asserted-by":"publisher","unstructured":"Pettai M, Laud P (2015) Combining differential privacy and secure multiparty computation. In: Proceedings of the 31st Annual Computer Security Applications Conference. ACSAC \u201915, pp. 421\u2013430. Association for Computing Machinery, New York, NY, USA. https:\/\/doi.org\/10.1145\/2818000.2818027","DOI":"10.1145\/2818000.2818027"},{"key":"1673_CR26","unstructured":"R Core Team (2021) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. R Foundation for Statistical Computing. https:\/\/www.R-project.org\/"},{"key":"1673_CR27","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755453","volume-title":"Semiparametric regression","author":"D Ruppert","year":"2003","unstructured":"Ruppert D, Wand MP, Carroll RJ (2003) Semiparametric regression. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, New York"},{"issue":"1\u20132","key":"1673_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1093\/biomet\/54.1-2.1","volume":"54","author":"HL Seal","year":"1967","unstructured":"Seal HL (1967) Studies in the History of Probability and Statistics. XV The historical development of the Gauss linear model. Biometrika 54(1\u20132):1\u201324. https:\/\/doi.org\/10.1093\/biomet\/54.1-2.1","journal-title":"Biometrika"},{"issue":"6","key":"1673_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3460427","volume":"54","author":"X Yin","year":"2021","unstructured":"Yin X, Zhu Y, Hu J (2021) A comprehensive survey of privacy-preserving federated learning: a taxonomy, review, and future directions. ACM Comput Surv 54(6):1\u201336. https:\/\/doi.org\/10.1145\/3460427","journal-title":"ACM Comput Surv"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-025-01673-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00180-025-01673-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-025-01673-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T08:40:46Z","timestamp":1763368846000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00180-025-01673-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,6]]},"references-count":29,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["1673"],"URL":"https:\/\/doi.org\/10.1007\/s00180-025-01673-8","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"type":"print","value":"0943-4062"},{"type":"electronic","value":"1613-9658"}],"subject":[],"published":{"date-parts":[[2025,10,6]]},"assertion":[{"value":"20 March 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 September 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 October 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}