Understanding alternating minimization for matrix completion

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2014, Pages 651-660

  Hardt, Moritz ^a  

^a IBM ALMADEN RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ITERATIVE METHODS; NUMBER THEORY;

ALTERNATING MINIMIZATION; CONVERGENCE ANALYSIS; DOMINANT SINGULAR VECTORS; ITERATIVE ALGORITHM; MATRIX COMPLETION; OPTIMIZATION PROBLEMS; SMOOTHED ANALYSIS; THEORETICAL GUARANTEES;

MATRIX ALGEBRA;

EID: 84920055127     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2014.75     Document Type: Conference Paper

References (24)

1. R. M. Bell and Y. Koren, "Scalable collaborative filtering with jointly derived neighborhood interpolation weights," in ICDM. IEEE Computer Society, 2007, pp. 43-52.
2. J. P. Haldar and D. Hernando, "Rank-constrained solutions to linear matrix equations using powerfactorization," IEEE Signal Process. Lett., vol. 16, no. 7, pp. 584-587, 2009.
3. Y. Koren, R. M. Bell, and C. Volinsky, "Matrix factorization techniques for recommender systems," IEEE Computer, vol. 42, no. 8, pp. 30-37, 2009.
4. E. J. Candes and B. Recht, "Exact matrix completion via convex optimization," Foundations of Computional Mathematics, vol. 9, pp. 717-772, December 2009.
5. B. Recht, "A simpler approach to matrix completion," Journal of Machine Learning Research, vol. 12, pp. 3413-3430, 2011.
6. E. J. Candes and T. Tao, "The power of convex relaxation: near-optimal matrix completion," IEEE Transactions on Information Theory, vol. 56, no. 5, pp. 2053-2080, 2010.
7. S. Ji and J. Ye, "An accelerated gradient method for trace norm minimization," in Proc. 26th ICML. ACM, 2009, p. 58.
8. R. Mazumder, T. Hastie, and R. Tibshirani, "Spectral regularization algorithms for learning large incomplete matrices," Journal of Machine Learning Research, vol. 11, pp. 2287-2322, 2010.
9. M. Jaggi and M. Sulovsky, "A simple algorithm for nuclear norm regularized problems," in Proc. 27th ICML. ACM, 2010, pp. 471-478.
10. H. Avron, S. Kale, S. P. Kasiviswanathan, and V. Sindhwani, "Efficient and practical stochastic subgradient descent for nuclear norm regularization," in Proc. 29th ICML. ACM, 2012.
11. C.-J. Hsieh and P. A. Olsen, "Nuclear norm minimization via active subspace selection," in Proc. 31st ICML. ACM, 2014.
12. P. Jain, P. Netrapalli, and S. Sanghavi, "Low-rank matrix completion using alternating minimization," in Proc. 45th Symposium on Theory of Computing (STOC). ACM, 2013, pp. 665-674.
13. R. H. Keshavan, "Efficient algorithms for collaborative filtering," Ph.D. dissertation, Stanford University, 2012.
14. S. Gunasekar, A. Acharya, N. Gaur, and J. Ghosh, "Noisy matrix completion using alternating minimization," in Proc. ECML PKDD. Springer, 2013, pp. 194-209.
15. M. Hardt, R. Meka, P. Raghavendra, and B. Weitz, "Computational limits for matrix completion," CoRR, vol. abs/1402.2331, 2014.
16. A. Sankar, D. A. Spielman, and S.-H. Teng, "Smoothed analysis of the condition numbers and growth factors of matrices," SIAM J. Matrix Analysis Applications, vol. 28, no. 2, pp. 446-476, 2006.
17. R. H. Keshavan, A. Montanari, and S. Oh, "Matrix completion from a few entries," IEEE Transactions on Information Theory, vol. 56, no. 6, pp. 2980-2998, 2010.
18. -, "Matrix completion from noisy entries," Journal of Machine Learning Research, vol. 11, pp. 2057-2078, 2010.
19. B. Recht and C. Re, "Parallel stochastic gradient algorithms for large-scale matrix completion," Math. Program. Comput., vol. 5, no. 2, pp. 201-226, 2013.
20. E. Hazan and S. Kale, "Projection-free online learning," in ICML. ACM, 2012.
21. M. Hardt and A. Roth, "Beating randomized response on incoherent matrices," in Proc. 44th Symposium on Theory of Computing (STOC). ACM, 2012, pp. 1255-1268.
22. -, "Beyond worst-case analysis in private singular vector computation," in Proc. 45th Symposium on Theory of Computing (STOC). ACM, 2013.
23. M. Hardt, "Robust subspace iteration and privacy-preserving spectral analysis," arXiv, vol. 1311:2495, 2013.
24. P. Zhu and A. V. Knyazev, "Angles between subspaces and their tangents," Arxiv preprint arXiv:1209.0523, 2012.