{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,3]],"date-time":"2025-05-03T05:13:08Z","timestamp":1746249188526,"version":"3.37.3"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T00:00:00Z","timestamp":1604275200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T00:00:00Z","timestamp":1604275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["IIS-1910492","CCF-1716400"],"award-info":[{"award-number":["IIS-1910492","CCF-1716400"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2020,12]]},"DOI":"10.1007\/s10994-020-05926-z","type":"journal-article","created":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T18:02:48Z","timestamp":1604340168000},"page":"2283-2311","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Robust high dimensional expectation maximization algorithm via trimmed hard thresholding"],"prefix":"10.1007","volume":"109","author":[{"given":"Di","family":"Wang","sequence":"first","affiliation":[]},{"given":"Xiangyu","family":"Guo","sequence":"additional","affiliation":[]},{"given":"Shi","family":"Li","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4908-0243","authenticated-orcid":false,"given":"Jinhui","family":"Xu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,11,2]]},"reference":[{"issue":"3","key":"5926_CR1","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1080\/00401706.1980.10486163","volume":"22","author":"M Aitkin","year":"1980","unstructured":"Aitkin, M., & Wilson, G. T. (1980). Mixture models, outliers, and the EM algorithm. Technometrics, 22(3), 325\u2013331.","journal-title":"Technometrics"},{"unstructured":"Alistarh, D., Allen-Zhu, Z., & Li, J. (2018). Byzantine stochastic gradient descent. In Advances in neural information processing systems, pp 4613\u20134623.","key":"5926_CR2"},{"unstructured":"Balakrishnan, S., Du, S.S., Li, J., & Singh, A. (2017a). Computationally efficient robust sparse estimation in high dimensions. In Conference on learning theory, pp 169\u2013212.","key":"5926_CR3"},{"issue":"1","key":"5926_CR4","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1214\/16-AOS1435","volume":"45","author":"S Balakrishnan","year":"2017","unstructured":"Balakrishnan, S., Wainwright, M. J., Yu, B., et al. (2017b). Statistical guarantees for the EM algorithm: From population to sample-based analysis. The Annals of Statistics, 45(1), 77\u2013120.","journal-title":"The Annals of Statistics"},{"issue":"3","key":"5926_CR5","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.acha.2009.04.002","volume":"27","author":"T Blumensath","year":"2009","unstructured":"Blumensath, T., & Davies, M. E. (2009). Iterative hard thresholding for compressed sensing. Applied and computational harmonic analysis, 27(3), 265\u2013274.","journal-title":"Applied and computational harmonic analysis"},{"key":"5926_CR6","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199535255.001.0001","volume-title":"Concentration inequalities: A nonasymptotic theory of independence","author":"S Boucheron","year":"2013","unstructured":"Boucheron, S., Lugosi, G., & Massart, P. (2013). Concentration inequalities: A nonasymptotic theory of independence. Oxford: Oxford University Press."},{"unstructured":"Chen, Y., Caramanis, C., & Mannor, S. (2013). Robust sparse regression under adversarial corruption. In International conference on machine learning, pp 774\u2013782.","key":"5926_CR7"},{"doi-asserted-by":"crossref","unstructured":"Chen, Y., Su, L., & Xu, J. (2017). Distributed statistical machine learning in adversarial settings: Byzantine gradient descent. Proceedings of the ACM on measurement and analysis of computing systems, 1(2), 44.","key":"5926_CR8","DOI":"10.1145\/3154503"},{"issue":"3","key":"5926_CR9","doi-asserted-by":"publisher","first-page":"1738","DOI":"10.1109\/TIT.2017.2773474","volume":"64","author":"Y Chen","year":"2018","unstructured":"Chen, Y., Yi, X., & Caramanis, C. (2018). Convex and nonconvex formulations for mixed regression with two components: Minimax optimal rates. IEEE Transactions on Information Theory, 64(3), 1738\u20131766.","journal-title":"IEEE Transactions on Information Theory"},{"unstructured":"Dalalyan, A.S., & Thompson, P. (2019). Outlier-robust estimation of a sparse linear model using $$\\ell _1$$-penalized huber\u2019s $$m$$-estimator. arXiv preprint arXiv:1904.06288.","key":"5926_CR10"},{"issue":"1","key":"5926_CR11","first-page":"20","volume":"28","author":"AP Dawid","year":"1979","unstructured":"Dawid, A. P., & Skene, A. M. (1979). Maximum likelihood estimation of observer error-rates using the EM algorithm. Journal of the Royal Statistical Society: Series C (Applied Statistics), 28(1), 20\u201328.","journal-title":"Journal of the Royal Statistical Society: Series C (Applied Statistics)"},{"doi-asserted-by":"crossref","unstructured":"Diakonikolas, I., Kamath, G., Kane, D.M., Li, J., Moitra, A., & Stewart, A. (2016). Robust estimators in high dimensions without the computational intractability. In 2016 IEEE 57th annual symposium on foundations of computer science (FOCS), IEEE, pp 655\u2013664.","key":"5926_CR12","DOI":"10.1109\/FOCS.2016.85"},{"doi-asserted-by":"crossref","unstructured":"Diakonikolas, I., Kane, D.M., & Stewart, A. (2017). Statistical query lower bounds for robust estimation of high-dimensional Gaussians and Gaussian mixtures. In 2017 IEEE 58th annual symposium on foundations of computer science (FOCS), IEEE, pp 73\u201384.","key":"5926_CR13","DOI":"10.1109\/FOCS.2017.16"},{"doi-asserted-by":"crossref","unstructured":"Diakonikolas, I., Kane, D.M., & Stewart, A. (2018). List-decodable robust mean estimation and learning mixtures of spherical gaussians. In Proceedings of the 50th annual ACM SIGACT symposium on theory of computing, ACM, pp 1047\u20131060.","key":"5926_CR14","DOI":"10.1145\/3188745.3188758"},{"unstructured":"Du, S.S., Balakrishnan, S., & Singh, A. (2017). Computationally efficient robust estimation of sparse functionals. arXiv preprint arXiv:1702.07709.","key":"5926_CR15"},{"issue":"10","key":"5926_CR16","doi-asserted-by":"publisher","first-page":"2150","DOI":"10.1080\/02664763.2013.807332","volume":"40","author":"S Faria","year":"2013","unstructured":"Faria, S., & Gon\u00e7alves, F. (2013). Financial data modeling by Poisson mixture regression. Journal of Applied Statistics, 40(10), 2150\u20132162.","journal-title":"Journal of Applied Statistics"},{"unstructured":"Holland, M.J. (2018). Robust descent using smoothed multiplicative noise. arXiv preprint arXiv:1810.06207.","key":"5926_CR17"},{"key":"5926_CR18","volume-title":"Robust statistics","author":"PJ Huber","year":"2011","unstructured":"Huber, P. J. (2011). Robust statistics. Berlin: Springer."},{"unstructured":"Johnson, R., & Zhang, T. (2013). Accelerating stochastic gradient descent using predictive variance reduction. In Advances in neural information processing systems, pp 315\u2013323.","key":"5926_CR19"},{"doi-asserted-by":"crossref","unstructured":"Laird, N.M. (2010). The em algorithm in genetics, genomics and public health. Statistical Science, 25(4), 450\u2013457.","key":"5926_CR20","DOI":"10.1214\/08-STS270"},{"unstructured":"Li, J. (2017). Robust sparse estimation tasks in high dimensions. arXiv preprint arXiv:1702.05860.","key":"5926_CR21"},{"unstructured":"Liu, L., Li, T., & Caramanis, C. (2019). High dimensional robust estimation of sparse models via trimmed hard thresholding. arXiv preprint arXiv:1901.08237.","key":"5926_CR22"},{"unstructured":"Loh, P.L., & Wainwright, M.J. (2011). High-dimensional regression with noisy and missing data: Provable guarantees with non-convexity. In Advances in neural information processing systems, pp 2726\u20132734.","key":"5926_CR23"},{"issue":"12","key":"5926_CR24","doi-asserted-by":"publisher","first-page":"2881","DOI":"10.1162\/089976600300014764","volume":"12","author":"J Ma","year":"2000","unstructured":"Ma, J., Xu, L., & Jordan, M. I. (2000). Asymptotic convergence rate of the EM algorithm for Gaussian mixtures. Neural Computation, 12(12), 2881\u20132907.","journal-title":"Neural Computation"},{"key":"5926_CR25","volume-title":"The EM algorithm and extensions","author":"G McLachlan","year":"2007","unstructured":"McLachlan, G., & Krishnan, T. (2007). The EM algorithm and extensions (Vol. 382). Hoboken: Wiley."},{"key":"5926_CR26","volume-title":"Introductory lectures on convex optimization: A basic course","author":"Y Nesterov","year":"2013","unstructured":"Nesterov, Y. (2013). Introductory lectures on convex optimization: A basic course (Vol. 87). Berlin: Springer Science & Business Media."},{"unstructured":"Prasad, A., Suggala, A.S., Balakrishnan, S., & Ravikumar, P. (2018). Robust estimation via robust gradient estimation. arXiv preprint arXiv:1802.06485.","key":"5926_CR27"},{"unstructured":"Suggala, A.S., Bhatia, K., Ravikumar, P., & Jain, P. (2019). Adaptive hard thresholding for near-optimal consistent robust regression. arXiv preprint arXiv:1903.08192.","key":"5926_CR28"},{"unstructured":"Thompson, P., & Dalalyan, A.S. (2018). Restricted eigenvalue property for corrupted gaussian designs. arXiv preprint arXiv:1805.08020.","key":"5926_CR29"},{"unstructured":"Vershynin, R. (2010). Introduction to the non-asymptotic analysis of random matrices. arXiv preprint arXiv:1011.3027.","key":"5926_CR30"},{"unstructured":"Wang, Z., Gu, Q., Ning, Y., Liu, H. (2015). High dimensional EM algorithm: Statistical optimization and asymptotic normality. In Advances in neural information processing systems, pp 2521\u20132529.","key":"5926_CR31"},{"issue":"1","key":"5926_CR32","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1214\/aos\/1176346060","volume":"11","author":"CJ Wu","year":"1983","unstructured":"Wu, C. J., et al. (1983). On the convergence properties of the EM algorithm. The Annals of statistics, 11(1), 95\u2013103.","journal-title":"The Annals of statistics"},{"issue":"11","key":"5926_CR33","doi-asserted-by":"publisher","first-page":"3950","DOI":"10.1016\/j.patcog.2012.04.031","volume":"45","author":"MS Yang","year":"2012","unstructured":"Yang, M. S., Lai, C. Y., & Lin, C. Y. (2012). A robust EM clustering algorithm for Gaussian mixture models. Pattern Recognition, 45(11), 3950\u20133961.","journal-title":"Pattern Recognition"},{"unstructured":"Yi, X., & Caramanis, C. (2015). Regularized em algorithms: A unified framework and statistical guarantees. In Advances in neural information processing systems, pp 1567\u20131575.","key":"5926_CR34"},{"unstructured":"Yin, D., Chen, Y., Ramchandran, K., & Bartlett, P. (2018). Byzantine-robust distributed learning: Towards optimal statistical rates. arXiv preprint arXiv:1803.01498.","key":"5926_CR35"},{"unstructured":"Zhu, R., Wang, L., Zhai, C., & Gu, Q. (2017). High-dimensional variance-reduced stochastic gradient expectation-maximization algorithm. In Proceedings of the 34th international conference on machine learning Volume 70, JMLR. org, pp 4180\u20134188.","key":"5926_CR36"}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-020-05926-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10994-020-05926-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-020-05926-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T01:03:48Z","timestamp":1635815028000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10994-020-05926-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,2]]},"references-count":36,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["5926"],"URL":"https:\/\/doi.org\/10.1007\/s10994-020-05926-z","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"type":"print","value":"0885-6125"},{"type":"electronic","value":"1573-0565"}],"subject":[],"published":{"date-parts":[[2020,11,2]]},"assertion":[{"value":"16 April 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 July 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 October 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 November 2020","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"}]}}