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We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers.
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Boaz Barak and Ankur Moitra, Noisy tensor completion via the sum-of-squares hierarchy , COLT, JMLR Workshop and Conference Proceedings, vol. 49, JMLR.org, 2016, pp. 417–445
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Ilias Diakonikolas, Gautam Kamath, Daniel M. Kane, Jerry Li, Ankur Moitra, and Alistair Stewart, Robust estimators in high dimensions without the computational intractability , FOCS, IEEE Computer Society, 2016, pp. 655–664
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Navin Goyal, Santosh Vempala, and Ying Xiao, Fourier PCA , CoRR abs/1306.5825
2013
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Daniel Hsu and Sham M. Kakade, Learning mixtures of spherical Gaussians: moment methods and spectral decompositions , ITCS’13—Proceedings of the 2013 ACM Conference on Innovations in Theoretical Computer Science, ACM, New York, 2013, pp. 11–19. MR 3385380
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Daniel J. Hsu and Sham M. Kakade, Learning mixtures of spherical gaussians: moment methods and spectral decompositions , ITCS, ACM, 2013, pp. 11–20
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Animashree Anandkumar, Rong Ge, Daniel J. Hsu, Sham M. Kakade, and Matus Telgarsky, Tensor decompositions for learning latent variable models , Journal of Machine Learning Research 15
2014
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Aditya Bhaskara, Moses Charikar, Ankur Moitra, and Aravindan Vijayaraghavan, Smoothed analysis of tensor decompositions , STOC, ACM, 2014, pp. 594–603
2014
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Boaz Barak, Jonathan A. Kelner, and David Steurer, Dictionary learning and tensor decomposition via the sum-of-squares method , STOC, ACM, 2015, pp. 143–151
2015
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Rong Ge and Tengyu Ma, Decomposing overcomplete 3rd order tensors using sum-of-squares algorithms , APPROX-RANDOM, LIPIcs, vol. 40, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2015, pp. 829–849
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Kevin A. Lai, Anup B. Rao, and Santosh Vempala, Agnostic estimation of mean and covariance , FOCS, IEEE Computer Society, 2016, pp. 665–674
2016
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Tengyu Ma, Jonathan Shi, and David Steurer, Polynomial-time tensor decompositions with sum-of-squares , FOCS, IEEE Computer Society, 2016, pp. 438–446
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Yeshwanth Cherapanamjeri, Prateek Jain, and Praneeth Netrapalli, Thresholding based outlier robust PCA , COLT, Proceedings of Machine Learning Research, vol. 65, PMLR, 2017, pp. 593–628
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Moses Charikar, Jacob Steinhardt, and Gregory Valiant, Learning from untrusted data , STOC, ACM, 2017, pp. 47–60
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