{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:32:25Z","timestamp":1740123145973,"version":"3.37.3"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T00:00:00Z","timestamp":1629072000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T00:00:00Z","timestamp":1629072000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation: NSF","doi-asserted-by":"crossref","award":["DMS-1749857","CCF-1740707"],"award-info":[{"award-number":["DMS-1749857","CCF-1740707"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s10994-021-06040-4","type":"journal-article","created":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T21:02:21Z","timestamp":1629147741000},"page":"2763-2834","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Provable training set debugging for linear regression"],"prefix":"10.1007","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1025-6061","authenticated-orcid":false,"given":"Xiaomin","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaojin","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Po-Ling","family":"Loh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,16]]},"reference":[{"key":"6040_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1214\/ECP.v20-3829","volume":"20","author":"R Adamczak","year":"2015","unstructured":"Adamczak, R. (2015). A note on the Hanson-Wright inequality for random vectors with dependencies. Electronic Communications in Probability, 20, 1\u201313.","journal-title":"Electronic Communications in Probability"},{"key":"6040_CR2","unstructured":"Cadamuro, G., Gilad-Bachrach, R., & Zhu, X. (2016). Debugging machine learning models. In ICML Workshop on Reliable Machine Learning in the Wild."},{"key":"6040_CR3","unstructured":"Chakraborty, A., Alam, M., Dey, V., Chattopadhyay, A., & Mukhopadhyay, D. (2018). Adversarial attacks and defences: A survey. arXiv preprint arXiv:1810.00069"},{"key":"6040_CR4","unstructured":"Fergus, R., Weiss, Y., & Torralba, A. (2009). Semi-supervised learning in gigantic image collections. In NIPS (Vol.\u00a01, p.\u00a02), Citeseer."},{"issue":"2","key":"6040_CR5","doi-asserted-by":"publisher","first-page":"1223","DOI":"10.1109\/TIT.2013.2293654","volume":"60","author":"R Foygel","year":"2014","unstructured":"Foygel, R., & Mackey, L. (2014). Corrupted sensing: Novel guarantees for separating structured signals. IEEE Transactions on Information Theory, 60(2), 1223\u20131247.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"6040_CR6","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1137\/1023004","volume":"23","author":"HV Henderson","year":"1981","unstructured":"Henderson, H. V., & Searle, S. R. (1981). On deriving the inverse of a sum of matrices. SIAM Review, 23(1), 53\u201360.","journal-title":"SIAM Review"},{"key":"6040_CR7","doi-asserted-by":"crossref","unstructured":"Hoeffding, W. (1994). Probability inequalities for sums of bounded random variables. In The Collected Works of Wassily Hoeffding (pp. 409\u2013426), Springer.","DOI":"10.1007\/978-1-4612-0865-5_26"},{"key":"6040_CR8","unstructured":"Horn, R. A., & Johnson, C. R. (1994). Topics in matrix analysis. Cambridge University Press."},{"key":"6040_CR9","doi-asserted-by":"crossref","unstructured":"Huber, P., & Ronchetti, E. (2011). Robust statistics. Wiley Series in Probability and Statistics. Wiley.","DOI":"10.1002\/9781118018255"},{"issue":"2","key":"6040_CR10","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1080\/00029890.2004.11920060","volume":"111","author":"SG Hwang","year":"2004","unstructured":"Hwang, S. G. (2004). Cauchy\u2019s interlace theorem for eigenvalues of Hermitian matrices. The American Mathematical Monthly, 111(2), 157\u2013159.","journal-title":"The American Mathematical Monthly"},{"issue":"1","key":"6040_CR11","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1214\/07-AOS582","volume":"37","author":"N Meinshausen","year":"2009","unstructured":"Meinshausen, N., & Yu, B. (2009). Lasso-type recovery of sparse representations for high-dimensional data. The Annals of Statistics, 37(1), 246\u2013270.","journal-title":"The Annals of Statistics"},{"issue":"59","key":"6040_CR12","doi-asserted-by":"publisher","first-page":"2036","DOI":"10.1109\/TIT.2012.2232347","volume":"4","author":"NH Nguyen","year":"2013","unstructured":"Nguyen, N. H., & Tran, T. D. (2013). Robust Lasso with missing and grossly corrupted observations. IEEE Transactions on Information Theory, 4(59), 2036\u20132058.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"3","key":"6040_CR13","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.1214\/09-AOS691","volume":"38","author":"P Ravikumar","year":"2010","unstructured":"Ravikumar, P., Wainwright, M. J., & Lafferty, J. D. (2010). High-dimensional Ising model selection using $$\\ell _1$$-regularized logistic regression. The Annals of Statistics, 38(3), 1287\u20131319.","journal-title":"The Annals of Statistics"},{"issue":"1","key":"6040_CR14","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s10618-005-0024-4","volume":"12","author":"PJ Rousseeuw","year":"2006","unstructured":"Rousseeuw, P. J., & Van Driessen, K. (2006). Computing LTS regression for large data sets. Data Mining and Knowledge Discovery, 12(1), 29\u201345.","journal-title":"Data Mining and Knowledge Discovery"},{"key":"6040_CR15","unstructured":"Sasai, T., & Fujisawa, H. (2020). Robust estimation with Lasso when outputs are adversarially contaminated. arXiv preprint arXiv:2004.05990"},{"key":"6040_CR16","doi-asserted-by":"crossref","unstructured":"Seber, G. A. F. (2008). A matrix handbook for statisticians (Vol. 15). Wiley.","DOI":"10.1002\/9780470226797"},{"issue":"494","key":"6040_CR17","doi-asserted-by":"publisher","first-page":"626","DOI":"10.1198\/jasa.2011.tm10390","volume":"106","author":"Y She","year":"2011","unstructured":"She, Y., & Owen, A. B. (2011). Outlier detection using nonconvex penalized regression. Journal of the American Statistical Association, 106(494), 626\u2013639.","journal-title":"Journal of the American Statistical Association"},{"key":"6040_CR18","unstructured":"Slawski, M., & Ben-David, E. (2017). Linear regression with sparsely permuted data. arXiv preprint arXiv:1710.06030"},{"issue":"2","key":"6040_CR19","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s10898-015-0274-7","volume":"66","author":"Y Tang","year":"2016","unstructured":"Tang, Y., Richard, J. P. P., & Smith, J. C. (2016). A class of algorithms for mixed-integer bilevel min\u2013max optimization. Journal of Global Optimization, 66(2), 225\u2013262.","journal-title":"Journal of Global Optimization"},{"key":"6040_CR20","doi-asserted-by":"crossref","unstructured":"Veit, A., Alldrin, N., Chechik, G., Krasin, I., Gupta, A., & Belongie, S. (2017). Learning from noisy large-scale datasets with minimal supervision. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 839\u2013847).","DOI":"10.1109\/CVPR.2017.696"},{"key":"6040_CR21","unstructured":"Vershynin, R. (2010). Introduction to the non-asymptotic analysis of random matrices. arXiv preprint arXiv:1011.3027"},{"key":"6040_CR22","doi-asserted-by":"crossref","unstructured":"Vershynin, R. (2018). High-dimensional probability: An introduction with applications in data science (Vol. 47). Cambridge University Press.","DOI":"10.1017\/9781108231596"},{"issue":"5","key":"6040_CR23","doi-asserted-by":"publisher","first-page":"2183","DOI":"10.1109\/TIT.2009.2016018","volume":"55","author":"MJ Wainwright","year":"2009","unstructured":"Wainwright, M. J. (2009). Sharp thresholds for high-dimensional and noisy sparsity recovery using $$\\ell _1$$-constrained quadratic programming (Lasso). IEEE Transactions on Information Theory, 55(5), 2183\u20132202.","journal-title":"IEEE Transactions on Information Theory"},{"key":"6040_CR24","doi-asserted-by":"crossref","unstructured":"Wainwright, M. J. (2019). High-dimensional statistics: A non-asymptotic viewpoint (Vol. 48). Cambridge University Press.","DOI":"10.1017\/9781108627771"},{"key":"6040_CR25","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/j.cor.2013.07.016","volume":"41","author":"P Xu","year":"2014","unstructured":"Xu, P., & Wang, L. (2014). An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions. Computers & Operations Research, 41, 309\u2013318.","journal-title":"Computers & Operations Research"},{"key":"6040_CR26","unstructured":"Zeng, B., & An, Y. (2014). Solving bilevel mixed integer program by reformulations and decomposition. Optimization Online (pp. 1\u201334)."},{"key":"6040_CR27","doi-asserted-by":"crossref","unstructured":"Zhang, X., Zhu, X., & Wright, S. (2018). Training set debugging using trusted items. In Proceedings of the AAAI conference on artificial intelligence (Vol.\u00a032).","DOI":"10.1609\/aaai.v32i1.11610"}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-021-06040-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10994-021-06040-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-021-06040-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T00:03:13Z","timestamp":1660608193000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10994-021-06040-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,16]]},"references-count":27,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["6040"],"URL":"https:\/\/doi.org\/10.1007\/s10994-021-06040-4","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"type":"print","value":"0885-6125"},{"type":"electronic","value":"1573-0565"}],"subject":[],"published":{"date-parts":[[2021,8,16]]},"assertion":[{"value":"28 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 August 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}