Provable ICA with unknown Gaussian noise, with implications for Gaussian mixtures and autoencoders

Advances in Neural Information Processing Systems

Volumn 3, Issue , 2012, Pages 2375-2383

  Arora, Sanjeev ^a   Ge, Rong ^a   Moitra, Ankur ^b   Sachdeva, Sushant ^a  

^a Princeton University   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOENCODERS; GAUSSIAN MIXTURES; GAUSSIAN RANDOM VARIABLE; INDEPENDENT COMPONENT ANALYSIS(ICA); LOCAL OPTIMA; PERFORMANCE GUARANTEES; RUNNING TIME; SAMPLE COMPLEXITY;

ALGORITHMS; COVARIANCE MATRIX; GAUSSIAN NOISE (ELECTRONIC); RANDOM VARIABLES;

INDEPENDENT COMPONENT ANALYSIS;

EID: 84877781888     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (22)

1. P. Comon. Independent component analysis: a new concept? Signal Processing, pp. 287-314, 1994. 1, 1.1
2. A. Hyvarinen, J. Karhunen, E. Oja. Independent Component Analysis. Wiley: New York, 2001. 1
3. A. Hyvarinen, E. Oja. Independent component analysis: algorithms and applications. Neural Networks, pp. 411-430, 2000. 1
4. P. J. Huber. Projection pursuit. Annals of Statistics pp. 435-475, 1985. 1
5. A. Frieze, M. Jerrum, R. Kannan. Learning linear transformations. FOCS, pp. 359-368, 1996. 1, 1.1, 4.1, 4.4, 5, 5.1
6. A. Anandkumar, D. Foster, D. Hsu, S. Kakade, Y. Liu. Two SVDs suffice: spectral decompositions for probabilistic topic modeling and latent Dirichlet allocation. Arxiv:abs/1203.0697, 2012. 1
7. D. Hsu, S. Kakade. Learning mixtures of spherical Gaussians: moment methods and spectral decompositions. Arxiv:abs/1206.5766, 2012. 1
8. L. De Lathauwer; J. Castaing; J.-F. Cardoso, Fourth-Order Cumulant-Based Blind Identification of Underdetermined Mixtures, Signal Processing, IEEE Transactions on, vol.55, no.6, pp.2965-2973, June 2007 1
9. A.P. Dempster, N.M. Laird, and D.B. Rubin. Maximum likelihood from incomplete data via the EM Algorithm. Journal of the Royal Statistical Society Series B, pp. 1-38, 1977. 1
10. S. Dasgupta. Learning mixtures of Gaussians. FOCS pp. 634-644, 1999. 1
11. S. Arora and R. Kannan. Learning mixtures of separated nonspherical Gaussians. Annals of Applied Probability, pp. 69-92, 2005. 1
12. M. Belkin and K. Sinha. Polynomial learning of distribution families. FOCS pp. 103-112, 2010. 1
13. A. T. Kalai, A. Moitra, and G. Valiant. Efficiently learning mixtures of two Gaussians. STOC pp. 553-562, 2010. 1
14. A. Moitra and G. Valiant. Setting the polynomial learnability of mixtures of Gaussians. FOCS pp. 93-102, 2010. 1
15. G. Hinton, R. Salakhutdinov. Reducing the dimensionality of data with neural networks. Science pp. 504-507, 2006. 1
16. Y. Bengio. Learning deep architectures for AI. Foundations and Trends in Machine Learning, pp. 1-127, 2009. 1
17. G. E. Hinton. A Practical Guide to Training Restricted Boltzmann Machines, Version 1, UTML TR 2010-003, Department of Computer Science, University of Toronto, August 2010 1
18. Y. Freund, D. Haussler. Unsupervised Learning of Distributions on Binary Vectors using Two Layer Networks University of California at Santa Cruz, Santa Cruz, CA, 1994 1
19. S. Cruces, L. Castedo, A. Cichocki, Robust blind source separation algorithms using cumulants, Neurocomputing, Volume 49, Issues 14, pp 87-118, 2002. 1.1
20. L., De Lathauwer; B., De Moor; J. Vandewalle. Independent component analysis based on higher-order statistics only Proceedings of 8th IEEE Signal ProcessingWorkshop on Statistical Signal and Array Processing, 1996. 1.1
21. S. Vempala, Y. Xiao. Structure from local optima: learning subspace juntas via higher order PCA. Arxiv:abs/1108.3329, 2011. 1.1
22. M. Kendall, A. Stuart. The Advanced Theory of Statistics Charles Griffin and Company, 1958.