Smoothed analysis of tensor decompositions

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2014, Pages 594-603

  Bhaskara, Aditya ^a   Charikar, Moses ^b   Moitra, Ankur ^c   Vijayaraghavan, Aravindan ^d  

^a GOOGLE INC   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; MATRIX ALGEBRA; MIXTURES; POLYNOMIALS;

ASSOCIATED MATRICES; EFFICIENT DECOMPOSITION; LINEARLY INDEPENDENTS; LOW-RANK DECOMPOSITION; MULTI-VIEW MODELS; POLYNOMIAL NUMBER; TECHNICAL CONTRIBUTION; TENSOR DECOMPOSITION;

TENSORS;

EID: 84904369044     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2591796.2591881     Document Type: Conference Paper

References (39)

1. E. Allman, C. Matias and J. Rhodes. Identifiability of Parameters in Latent Structure Models with many Observed Variables. Annals of Statistics, pages 3099-3132, 2009.
2. A. Anandkumar, D. Hsu and S. Kakade. A method of moments for mixture models and hidden Markov models. In COLT 2012.
3. A. Anandkumar, R. Ge, D. Hsu and S. Kakade. A Tensor Spectral Approach to Learning Mixed Membership Community Models. In COLT 2013.
4. A. Anandkumar, R. Ge, D. Hsu, S. Kakade and M. Telgarsky. Tensor Decompositions for Learning Latent Variable Models. arxiv:1210.7559, 2012.
5. A. Anandkumar, D. Foster, D. Hsu, S. Kakade, Y. Liu. A Spectral Algorithm for Latent Dirichlet Allocation. In NIPS, pages 926-934, 2012.
6. S. Arora, R. Ge, A. Moitra and S. Sachdeva. Provable ICA with Unknown Gaussian Noise, and Implications for Gaussian Mixtures and Autoencoders. In NIPS, pages 2384-2392, 2012.
7. M. Belkin, L. Rademacher and J. Voss. Bling Signal Separation in the Presence of Gaussian Noise. In COLT 2013.
8. M. Belkin and K. Sinha. Polynomial Learning of Distribution Families. In FOCS, pages 103-112, 2010.
9. A. Bhaskara, M. Charikar and A. Vijayaraghavan. Uniqueness of Tensor Decompositions with Applications to Polynomial Identifiability. arxiv:1304.8087, 2013.
10. A. Bhaskara, M. Charikar, A. Moitra and A. Vijayaraghavan. Smoothed Analysis of Tensor Decompositions. arxiv:1311.3651, 2013.
11. J. Chang. Full Reconstruction of Markov Models on Evolutionary Trees: Identifiability and Consistency. Mathematical Biosciences, pages 51-73, 1996.
12. P. Comon. Independent Component Analysis: A New Concept? Signal Processing, pages 287-314, 1994.
13. S. Dasgupta. Learning Mixtures of Gaussians. In FOCS, pages 634-644, 1999.
14. L. De Lathauwer, J Castaing and J. Cardoso. Fourth-order Cumulant-based Blind Identification of Underdetermined Mixtures. IEEE Trans. on Signal Processing, 55(6):2965-2973, 2007.
15. J. Feldman, R. A. Servedio, and R. O'Donnell. PAC Learning Axis-aligned Mixtures of Gaussians with No Separation Assumption. In COLT, pages 20-34, 2006.
16. A. Frieze, M. Jerrum, R. Kannan. Learning Linear Transformations. In FOCS, pages 359-368, 1996.
17. N. Goyal, S. Vempala and Y. Xiao. Fourier PCA. In STOC, 2014 (this proceedings).
18. R. Harshman. Foundations of the PARFAC procedure: model and conditions for an 'explanatory' multi-mode factor analysis. UCLA Working Papers in Phonetics, pages 1-84, 1970.
19. J. Håstad. Tensor Rank is NP-Complete. Journal of Algorithms, pages 644-654, 1990.
20. C. Hillar and L-H. Lim. Most Tensor Problems are NP-Hard. arxiv:0911.1393v4, 2013.
21. R. Horn and C. Johnson. Matrix Analysis. Cambridge University Press, 1990.
22. D. Hsu and S. Kakade. Learning Mixtures of Spherical Gaussians: Moment Methods and Spectral Decompositions. In ITCS, pages 11-20, 2013.
23. A. Hyvärinen, J. Karhunen and E. Oja. Independent Component Analysis. Wiley Interscience, 2001.
24. A. T. Kalai, A. Moitra, and G. Valiant. Efficiently Learning Mixtures of Two Gaussians. In STOC, pages 553-562, 2010.
25. A. T. Kalai, A. Samorodnitsky and S-H Teng. Learning and Smoothed Analysis. In FOCS, pages 395-404, 2009.
26. J. Kruskal. Three-way Arrays: Rank and Uniqueness of Trilinear Decompositions. Linear Algebra and Applications, 18:95-138, 1977.
27. S. Leurgans, R. Ross and R. Abel. A Decomposition for Three-way Arrays. SIAM Journal on Matrix Analysis and Applications, 14(4):1064-1083, 1993.
28. B. Lindsay. Mixture Models: Theory, Geometry and Applications. Institute for Mathematical Statistics, 1995.
29. P. McCullagh. Tensor Methods in Statistics. Chapman and Hall/CRC, 1987.
30. A. Moitra and G. Valiant. Setting the Polynomial Learnability of Mixtures of Gaussians. In FOCS, pages 93-102, 2010.
31. E. Mossel and S. Roch. Learning Nonsingular Phylogenies and Hidden Markov Models. In STOC, pages 366-375, 2005.
32. Y. Rabani, L. Schulman and C. Swamy. Learning mixtures of arbitrary distributions over large discrete domains. In ITCS 2014.
33. C. Spearman. General Intelligence. American Journal of Psychology, pages 201-293, 1904.
34. D.A. Spielman, S.H. Teng. Smoothed Analysis of Algorithms: Why the Simplex Algorithm usually takes Polynomial Time. Journal of the ACM, pages 385-463, 2004.
35. D.A. Spielman, S.H. Teng. Smoothed Analysis: An Attempt to Explain the Behavior of Algorithms in Practice. Communications of the ACM, pages 76-84, 2009.
36. A. Stegeman and P. Comon. Subtracting a Best Rank-1 Approximation may Increase Tensor Rank. Linear Algebra and Its Applications, pages 1276-1300, 2010.
37. H. Teicher. Identifiability of Mixtures. Annals of Mathematical Statistics, pages 244-248, 1961.
38. S. Vempala, Y. Xiao. Structure from Local Optima: Learning Subspace Juntas via Higher Order PCA. Arxiv:abs/1108.3329, 2011.
39. P. Wedin. Perturbation Bounds in Connection with Singular Value Decompositions. BIT, 12:99-111, 1972.