Low-rank matrix and tensor completion via adaptive sampling

Advances in Neural Information Processing Systems

Volumn , Issue , 2013, Pages

  Krishnamurthy, Akshay ^a   Singh, Aarti ^a  

^a Carnegie Mellon University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

RECOVERY; TENSORS;

ADAPTIVE SAMPLING; ADAPTIVITY; COLUMN SPACE; LOW-RANK MATRICES; N-MATRIX; NOVEL ALGORITHM; PERFORMANCE GUARANTEES; TENSOR COMPLETION;

ALGORITHMS;

EID: 84899013687     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (24)

1. Dimitris Achlioptas and Frank Mcsherry. Fast computation of low-rank matrix approximations. Journal of the ACM (JACM), 54(2):9, 2007.
2. Laura Balzano, Benjamin Recht, and Robert Nowak. High-dimensional matched subspace detection when data are missing. In Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on, pages 1638-1642. IEEE, 2010.
3. Christos Boutsidis, Michael W Mahoney, and Petros Drineas. An improved approximation algorithm for the column subset selection problem. In Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 968-977. Society for Industrial and Applied Mathematics, 2009.
4. Jian-Feng Cai, Emmanuel J Candès, and Zuowei Shen. A singular value thresholding algorithm for matrix completion. SIAM Journal on Optimization, 20(4):1956-1982, 2010.
5. Emmanuel J Candes and Yaniv Plan. Matrix completion with noise. Proceedings of the IEEE, 98(6):925-936, 2010.
6. Emmanuel J Candès and Benjamin Recht. Exact matrix completion via convex optimization. Foundations of Computational mathematics, 9(6):717-772, 2009.
7. Emmanuel J Candès and Terence Tao. The power of convex relaxation: Near-optimal matrix completion. Information Theory, IEEE Transactions on, 56(5):2053-2080, 2010.
8. Yudong Chen, Srinadh Bhojanapalli, Sujay Sanghavi, and Rachel Ward. Coherent matrix completion. arXiv preprint arXiv:1306.2979, 2013.
9. Mark A Davenport and Ery Arias-Castro. Compressive binary search. In Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on, pages 1827-1831. IEEE, 2012.
10. Amit Deshpande, Luis Rademacher, Santosh Vempala, and GrantWang. Matrix approximation and projective clustering via volume sampling. Theory of Computing, 2:225-247, 2006.
11. Silvia Gandy, Benjamin Recht, and Isao Yamada. Tensor completion and low-n-rank tensor recovery via convex optimization. Inverse Problems, 27(2):025010, 2011.
12. Alex Gittens. The spectral norm error of the naive nystrom extension. arXiv preprint arXiv:1110.5305, 2011.
13. David Gross. Recovering low-rank matrices from few coefficients in any basis. Information Theory, IEEE Transactions on, 57(3):1548-1566, 2011.
14. Venkatesan Guruswami and Ali Kemal Sinop. Optimal column-based low-rank matrix reconstruction. In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1207-1214. SIAM, 2012.
15. Jarvis D Haupt, Richard G Baraniuk, Rui M Castro, and Robert D Nowak. Compressive distilled sensing: Sparse recovery using adaptivity in compressive measurements. In Signals, Systems and Computers, 2009 Conference Record of the Forty-Third Asilomar Conference on, pages 1551-1555. IEEE, 2009.
16. Jun He, Laura Balzano, and John Lui. Online robust subspace tracking from partial information. arXiv preprint arXiv:1109.3827, 2011.
17. Raghunandan H Keshavan, Andrea Montanari, and Sewoong Oh. Matrix completion from noisy entries. The Journal of Machine Learning Research, 99:2057-2078, 2010.
18. Sanjiv Kumar, Mehryar Mohri, and Ameet Talwalkar. Sampling methods for the nyström method. The Journal of Machine Learning Research, 98888:981-1006, 2012.
19. Béatrice Laurent and Pascal Massart. Adaptive estimation of a quadratic functional by model selection. The annals of Statistics, 28(5):1302-1338, 2000.
20. Sahand Negahban and Martin J Wainwright. Restricted strong convexity and weighted matrix completion: Optimal bounds with noise. The Journal of Machine Learning Research, 2012.
21. Benjamin Recht. A simpler approach to matrix completion. The Journal of Machine Learning Research, 7777777:3413-3430, 2011.
22. Ryota Tomioka, Kohei Hayashi, and Hisashi Kashima. Estimation of low-rank tensors via convex optimization. arXiv preprint arXiv:1010.0789, 2010.
23. Ryota Tomioka, Taiji Suzuki, Kohei Hayashi, and Hisashi Kashima. Statistical performance of convex tensor decomposition. In Advances in Neural Information Processing Systems, pages 972-980, 2011.
24. Roman Vershynin. Introduction to the non-asymptotic analysis of random matrices. arXiv preprint arXiv:1011.3027, 2010.