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We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy.
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Anima Anandkumar, Dean P. Foster, Daniel J. Hsu, Sham Kakade, and Yi-Kai Liu, A spectral algorithm for latent dirichlet allocation , NIPS, 2012, pp. 926–934
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Joel A. Tropp, User-friendly tail bounds for sums of random matrices , Foundations of Computational Mathematics 12
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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
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Aditya Bhaskara, Moses Charikar, Ankur Moitra, and Aravindan Vijayaraghavan, Smoothed analysis of tensor decompositions , STOC, ACM, 2014, pp. 594–603
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Moritz Hardt and Eric Price, The noisy power method: A meta algorithm with applications , NIPS, 2014, pp. 2861–2869
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Sanjeev Arora, Rong Ge, Tengyu Ma, and Ankur Moitra, Simple, efficient, and neural algorithms for sparse coding , COLT, JMLR Workshop and Conference Proceedings, vol. 40, JMLR.org, 2015, pp. 113–149
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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
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Cited alongside, same era.
Animashree Anandkumar, Rong Ge, Daniel J. Hsu, and Sham Kakade, A tensor spectral approach to learning mixed membership community models , COLT, JMLR Workshop and Conference Proceedings, vol. 30, JMLR.org, 2013, pp. 867–881
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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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Alekh Agarwal, Animashree Anandkumar, Prateek Jain, Praneeth Netrapalli, and Rashish Tandon, Learning sparsely used overcomplete dictionaries , COLT, JMLR Workshop and Conference Proceedings, vol. 35, JMLR.org, 2014, pp. 123–137
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Richard A Harshman, Foundations of the parafac procedure: Models and conditions for an" explanatory" multi-modal factor analysis
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2016
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Elad Hazan and Tengyu Ma, A non-generative framework and convex relaxations for unsupervised learning , NIPS, 2016, pp. 3306–3314
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
2016
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