Latent variable graphical model selection via convex optimization

2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010

Volumn , Issue , 2010, Pages 1610-1613

  Chandrasekaran, Venkat ^a   Parrilo, Pablo A ^a   Willsky, Alan S ^a  

^a Department of Electrical Engineering and Computer Science   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC VARIETIES; CONDITIONAL GRAPHICAL MODEL; CONDITIONAL STATISTICS; CONVEX PROGRAMS; DIMENSIONALITY REDUCTION; GAUSSIANS; GEOMETRIC PROPERTIES; GRAPHICAL MODEL; GRAPHICAL MODELING; HIGH-DIMENSIONAL; LATENT VARIABLE; LOW-RANK MATRICES; MODEL SELECTION; MODELING FRAMEWORKS; NATURAL CONDITIONS; NUMBER OF SAMPLES; REGULARIZER; SPARSE MATRICES; STATISTICAL MODELS; STATISTICAL STRUCTURES;

CONVEX OPTIMIZATION; EQUIVALENCE CLASSES; GRAPHIC METHODS; MAXIMUM LIKELIHOOD; SPEECH RECOGNITION;

RANDOM VARIABLES;

EID: 79952399531     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ALLERTON.2010.5707106     Document Type: Conference Paper

References (27)

1. ALLMAN, E. S., MATIAS, C., AND RHODES, J. A. (2009). Identifiability of parameters in latent structure models with many observed variables. Ann. Statistics. 37 3099-3132.
2. BICKEL, P. J. AND LEVINA, E. (2008). Regularized estimation of large covariance matrices. Ann. Statistics. 36 199-227.
3. BICKEL, P. J. AND LEVINA, E. (2008). Covariance regularization by thresholding. Ann. Statistics. 36 2577-2604.
4. CANDÈS, E. J., ROMBERG, J., AND TAO, T. (2006). Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Info. Theory. 52 489-509.
5. CANDÈS, E. J. AND RECHT, B. (2009). Exact matrix completion via convex optimization. Found. of Comput. Math.. 9 717-772.
6. CANDÈS, E. J., LI, X., MA, Y. AND WRIGHT, J. (2009). Robust principal component analysis? Preprint.
7. CHANDRASEKARAN, V., SANGHAVI, S., PARRILO, P. A. AND WILLSKY, A. S. (2009). Rank-sparsity incoherence for matrix decomposition. Preprint.
8. CHANDRASEKARAN, V., PARRILO, P. A. AND WILLSKY, A. S. (2010). Rank-sparsity incoherence for matrix decomposition. Preprint.
9. DEMPSTER, A. P., LAIRD, N. M., AND RUBIN, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Stat. Soc. B. 39 1-38.
10. 1-norm solution is also the sparsest solution. Comm. on Pure and Applied Math.. 59 797-829.
11. DONOHO, D. L. (2006). Compressed sensing. IEEE Trans. Info. Theory. 52 1289-1306.
12. ELIDAN, G., NACHMAN, I., AND FRIEDMAN, N. (2007). "Ideal Parent" structure learning for continuous variable Bayesian networks. J. Mach. Lear. Res.. 8 1799-1833.
13. EL KAROUI, N. (2008). Operator norm consistent estimation of large-dimensional sparse covariance matrices. Ann. Statistics. 36 2717-2756.
14. FAN, J., FAN, Y., AND LV, J. (2008). High dimensional covariance matrix estimation using a factor model. J. Econometrics. 147 186-197.
15. FAZEL, M. (2002). Matrix rank minimization with applications. PhD thesis, Dep. Elec. Eng., Stanford University. 2002.
16. HORN, R. A. AND JOHNSON, C. R. (1990). Matrix analysis. Cambridge University Press.
17. JOHNSTONE, I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Ann. Statistics. 29 295-327.
18. LAM, C. AND FAN, J. (2009). Sparsistency and rates of convergence in large covariance matrix estimation. Ann. Statistics. 37 4254-4278.
19. LEDOIT, O. AND WOLF, M. (2003). A well-conditioned estimator for large-dimensional covariance matrices. J. Multivar. Analysis. 88 365-411.
20. MARCENKO, V. A. AND PASTUR, L. A. (1967). Distributions of eigenvalues of some sets of random matrices. Math. USSR-Sb. 1 507-536.
21. MEINSHAUSEN, N. AND BUHLMANN, P. (2006). High dimensional graphs and variable selection with the Lasso. Ann. Statistics. 34 1436-1462.
22. 1-penalized log-determinant divergence. Preprint.
23. RECHT, B., FAZEL, M., AND PARRILO, P. A. (2009). Guaranteed minimum rank solutions to linear matrix equations via nuclear norm minimization. SIAM Review, to appear.
24. ROTHMAN, A. J., BICKEL, P. J., LEVINA, E., AND ZHU, J. (2008). Sparse permutation invariant covariance estimation. Elec. J. Statistics. 2 494-515.
25. WANG, C., SUN, D. AND TOH, K. C. (2009). Solving log-determinant optimization problems by a Newton-CG primal proximal point algorithm. Preprint.
26. WU, W. B. AND POURAHMADI, M. (2003). Nonparametric estimation of large covariance matrices of longitudinal data. Biometrika. 90 831-844.
27. ZHAO, P. AND YU, B. (2006). On model selection consistency of Lasso. J. Mach. Lear. Res.. 7 2541-2567.