Efficiently learning mixtures of two Gaussians

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2010, Pages 553-562

  Kalai, Adam Tauman ^a   Moitra, Ankur ^b   Valiant, Gregory ^c  

^a MICROSOFT RESEARCH   (United Kingdom)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

finite mixture models; Gaussians; method of moments

Indexed keywords

ARBITRARY MIXTURES; DATA POINTS; DENSITY ESTIMATION; EXPONENTIAL TIME; FINITE MIXTURE MODELS; GAUSSIANS; N-DIMENSIONAL PROBLEMS; ONE DIMENSION; ONE-DIMENSIONAL PROBLEM; OPTIMAL CLUSTERING; OVERLAP REGION; POLYNOMIAL DATA; POLYNOMIAL-TIME; POLYNOMIAL-TIME ALGORITHMS; TECHNICAL CHALLENGES; UNIVARIATE;

ALGORITHMS; COMPUTATION THEORY; ELASTIC MODULI; METHOD OF MOMENTS; POLYNOMIALS;

MIXTURES;

EID: 77954731171     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1806689.1806765     Document Type: Conference Paper

References (25)

1. D. Achlioptas and F. McSherry. On spectral learning of mixtures of distributions. In COLT, pages 458-469, 2005.
2. S. Arora and R. Kannan. Learning mixtures of arbitrary Gaussians. In STOC, pages 247-257, 2001.
3. M. Belkin and K. Sinha. Learning Gaussian mixtures with arbitrary separation. CoRR, 2009.
4. S. C. Brubaker and S. Vempala. Isotropic PCA and affine-invariant clustering. In FOCS, pages 551-560, 2008.
5. S. Dasgupta. Learning mixtures of Gaussians. In FOCS, pages 634-644, 1999.
6. S. Dasgupta, A. T. Kalai, and C. Monteleoni. Analysis of perceptron-based active learning. In COLT, pages 249-263, 2005.
7. S. Dasgupta and L. J. Schulman. A two-round variant of EM for Gaussian mixtures. In UAI, pages 152-159, 2000.
8. A. P. Dempster, N. M. Laird, and D. B. Rubin. Maximum likelihood from incomplete data via the EM Algorithm. J. Roy. Statist. Soc. Ser. B, 39:1-38, 1977.
9. A. Dinghas. Über eine klasse superadditiver mengenfunktionale von brunn-minkowski-lusternik-schem typus. Math. Zeitschr., 68:111-125, 1957.
10. 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.
11. A. A. Giannopoulos and V. D. Milman. Concentration property on probability spaces. Adv. Math., 156:77-106, 2000.
12. R. A. Hummel and B. C. Gidas. Zero crossings and the Heat Equation. Technical Report Number 111, Courant Institute of Mathematical Sciences at NYU, 1984.
13. R. Kannan, H. Salmasian, and S. Vempala. The spectral method for general mixture models. SIAM J. Comput., 38(3):1141-1156, 2008.
14. M. J. Kearns, Y. Mansour, D. Ron, R. Rubinfeld, R. E. Schapire, and L. Sellie. On the learnability of discrete distributions. In STOC, pages 273-282, 1994.
15. L. Leindler. On a certain converse of Hölder's Inequality ii. Acta Sci. Math. Szeged, 33:217-223, 1972.
16. B. Lindsay. Mixture models: theory, geometry and applications. American Statistical Association, 1995.
17. L. Lovász and S. Vempala. The geometry of logconcave functions and sampling algorithms. Random Struct. Algorithms, 30(3):307-358, 2007.
18. P. Macdonald. Personal Communication, 2010
19. K. Pearson. Contributions to the mathematical theory of evolution. Phil. Trans. R. Soc. Lond. A, 1894.
20. A. Prékopa. Logarithmic concave measures and functions. Acta. Sci. Math. Szeged, 34:335-343, 1973.
21. M. Rudelson. Random vectors in the isotropic position. J. Funct. Anal, 164:60-72, 1999.
22. H. Teicher. Identifiability of mixtures. Ann. Math. Statist., 32(1):244-248, 1961.
23. L. Valiant. A theory of the learnable. Comm. ACM, 27(11):1134-1142, 1984.
24. S. Vempala and G. Wang. A spectral algorithm for learning mixture models. J. Comput. Syst. Sci., 68(4):841-860, 2004.
25. C. F. J. Wu. On the convergence properties of the EM Algorithm. Ann. Stat., 11(1):95-103, 1983.