On the convexity in Kronecker structured covariance estimation

2012 IEEE Statistical Signal Processing Workshop, SSP 2012

Volumn , Issue , 2012, Pages 880-883

  Wiesel, Ami ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

covariance estimation; Geodesic convexity; Kronecker; log sum exp

Indexed keywords

CLASSICAL MODEL; CONVEX REGULARIZATIONS; COVARIANCE ESTIMATION; COVARIANCE MATRICES; GEODESIC CONVEXITY; KRONECKER; KRONECKER PRODUCT; LOG-SUM-EXP; NONCONVEX OPTIMIZATION; NUMBER OF SAMPLES; NUMERICAL SOLUTION; POSITIVE-DEFINITE MATRICES; RANDOM MATRIX; STRUCTURED COVARIANCE;

COMPUTER SIMULATION; CONVEX OPTIMIZATION; MAXIMUM LIKELIHOOD ESTIMATION; SIGNAL PROCESSING;

COVARIANCE MATRIX;

EID: 84868254293     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SSP.2012.6319848     Document Type: Conference Paper

References (12)

1. T. Rapcsak, "Geodesic convexity in nonlinear optimization," Journal of Optimization Theory and Applications, vol. 69, no. 1, pp. 169-183, 1991.
2. L. Liberti, "On a class of nonconvex problems where all local minima are global," Publications de l'Institut Mathematique, vol. 76, no. 90, pp. 101-109, 2004.
3. A. Wiesel, "Unified framework to regularized covari-ance estimation in scaled Gaussian models," IEEE Trans. on Signal Processing, vol. 60, no. 1, pp. 29-38, Jan. 2012.
4. A. Wiesel, "Geodesic convexity with applications to co-variance estimation," Submitted to IEEE Trans. on Signal Processing, available in www.cs.huji.ac.il/~amiw.
5. P. Dutilleul, "The MLE algorithm for the matrix normal distribution," Journal of statistical computation and simulation, vol. 64, no. 2, pp. 105-123, 1999.
6. N. Lu and D. L. Zimmerman, "The likelihood ratio test for a separable covariance matrix," Statistics and Probability Letters, vol. 73, no. 4, pp. 449-457, 2005. (Pubitemid 40876275)
7. K. Werner, M. Jansson, and P. Stoica, "On estimation of covariance matrices with Kronecker product structure," IEEE Trans. on Signal Processing, vol. 56, no. 2, pp. 478-491, 2008. (Pubitemid 351285047)
8. G.I. Allen and R. Tibshirani, "Transposable regularized covariance models with an application to missing data imputation," The Annals of Applied Statistics, vol. 4, no. 2, pp. 764-790, 2010.
9. Y. Zhang and J. Schneider, "Learning multiple tasks with a sparse matrix-normal penalty," Advances in Neural Information Processing Systems, 2010.
10. M. Srivastava, T. von Rosen, and D. von Rosen, "Models with a Kronecker product covariance structure: Estimation and testing," Mathematical Methods of Statistics, vol. 17, pp. 357-370, 2008.
11. T. Tsiligkaridis, A.O. Hero III, and S. Zhou, "Convergence properties of Kronecker graphical Lasso algorithms," Arxiv preprint arXiv:1204.0585, 2012.
12. Y. Chen, A. Wiesel, Y.C. Eldar, and A.O. Hero, "Shrinkage algorithms for MMSE covariance estimation," IEEE Trans. on Signal Processing, vol. 58, no. 10, pp. 5016-5029, 2010.