Model selection and estimation in the matrix normal graphical model

Journal of Multivariate Analysis

Volumn 107, Issue , 2012, Pages 119-140

  Yin, Jianxin ^a,b   Li, Hongzhe ^a,b  

^a RENMIN UNIVERSITY OF CHINA   (China)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Gaussian graphical model; Gene networks; High dimensional data; L 1 penalized likelihood; Matrix normal distribution; Sparsistency

Indexed keywords

EID: 84862805433     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2012.01.005     Document Type: Article

References (42)

1. Allen G. Comment on article by Hoff. Bayesian Analysis 2011, 6(2):197-202.
2. Allen G., Tibshirani R. Transposable regularized covariance models with an application to missing data imputation. The Annals of Applied Statistics 2010, 4(2):764-790.
3. G. Allen, R. Tibshirani, Inference with transposable data: modeling the effects of row and column correlations, Journal of the Royal Statistical Society, Series B (Theory & Methods) (2011) (in press).
4. Banerjee O., Ghaoui L.E., d'Aspremont A. Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data. Journal of Machine Learning Research 2008, 9:485-516.
5. Bickel P., Levina E. Regularized estimation of large covariance matrices. Annals of Statistics 2008, 36(1):199-227.
6. 1 minimization approach to sparse precision matrix estimation. Journal of the American Statistical Association 2011, 106:594-607.
7. Candes E., Tao T. The Dantzig selector: statistical estimation when p is much larger than n. Annals of Statistics 2007, 35:2313-2351.
8. Cressie N. Statistics for Spatial Data 1993, Wiley, New York.
9. Dahl J., Vandenberghe L., Roychowdhury V. Covariance selection for non-chordal graphs via chordal embedding. Optimization Methods and Software 2008, 23:501-520.
10. Dawid A. Some matrix-variate distribution theory: notational considerations and a Bayesian application. Biometrika 1981, 68:265-274.
11. Dutilleul P. The mle algorithm for the matrix normal distribution. Journal of Statistical Computation and Simulation 1999, 64:105-123.
12. Efron B. Are a set of microarrays independent of each other?. The Annals of Applied Statistics 2009, 13(3):922-942.
13. Fan J., Feng Y., Wu Y. Network exploration via the adaptive lasso and scad penalties. The Annals of Applied Statistics 2009, 3:521-541.
14. Fan J., Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 2001, 96:1348-1360.
15. Finn J.D. A General Model for Multivariate Analysis 1974, Holt, Rinehart and Winston, New York.
16. Friedman J., Hastie T., Tibshirani R. Sparse inverse covariance estimation with the graphical lasso. Biostatistics 2008, 9:432-441.
17. Graybill F.A. Matrices with Applications in Statistics 1983, Wadsworth, Belmont. second ed.
18. Gupta A., Nagar D. Matrix Variate Distributions. Monographs and Surveys in Pure and Applied Mathematics 1999, vol. 104. Chapman & Hall, CRC Press, Boca Raton, FL.
19. Hoff P. Separable covariance arrays via the Tucker product, with applications to multivariate relational data. Bayesian Analysis 2011, 6(2):179-196.
20. Holmes K., Roberts O., Thomas A., Cross M. Vascular endothelial growth factor receptor-2: structure, function, intracellular signalling and therapeutic inhibition. Cellular Signalling 2007, 19:2003-2012.
21. Huizenga H.M., De Munck J.C., Waldorp L.J., Grasman R. Spatiotemporal EEG/MEG source analysis based on a parametric noisecovariance model. IEEE Transactions on Biomedical Engineering 2002, 49:533-539.
22. Lam C., Fan J. Sparsistency and rates of convergence in large covariance matrices estimation. The Annals of Statistics 2009, 37:4254-4278.
23. Lauritzen S.L. Graphical Models 1996, Clarendon Press, Oxford.
24. Lehmann E. Theory of Point Estimation 1983, Wadsworth and Brooks/Cole, Pacific Grove, CA.
25. Li H., Gui J. Gradient directed regularization for sparse Gaussian concentration graphs, with applications to inference of genetic networks. Biostatistics 2006, 7:302-317.
26. Mardia K.V., Goodall C. Spatial-temporal analysis of multivariate environmental monitoring data. Multivariate Environmental Statistics 1993, 6:347-385.
27. Meinshausen N., Bühlmann P. High-dimensional graphs and variable selection with the lasso. Annals of Statistics 2006, 34:1436-1462.
28. Mitchell M., Genton M., Gumpertz M. A likelihood ratio test for separability of covariances. Journal of Multivariate Analysis 2006, 97(5):1025-1043.
29. Muralidharan O. Detecting column dependence when rows are correlated and estimating the strength of the row correlation. Electronic Journal of Statistics 2010, 4:1527-1546.
30. 1-penalized log-determinant divergence. Electronic Journal of Statistics 2011, 5:935-980.
31. Rothman A., Levina E., Zhu J. Generalized thresholding of large covariance matrices. Journal of the American Statistical Association 2009, 104:177-186.
32. Teng S., Huang H. A statistical framework to infer functional gene associations from multiple biologically interrelated microarray experiments. Journal of the American Statistical Association 2009, 104:465-473.
33. Tibshirani R. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B 1996, 58:267-288.
34. Timm N.H. Multivariate analysis of variance of repeated measurements. Handbook of Statistics 1980, 1:41-87.
35. Tucker L.R. The extension of factor analysis to three-dimensional matrices. Contributions to Mathematical Psychology 1964, Holt, Rinehart and Winston, New York. H. Gulliksen, N. Frederiksen (Eds.).
36. Wang H., West M. Bayesian analysis of matrix normal graphical models. Biometrika 2009, 96:821-834.
37. Whittaker J. Graphical Models in Applied Multivariate Analysis 1990, Wiley.
38. Yuan M. Sparse inverse covariance matrix estimation via linear programming. Journal of Machine Learning Research 2010, 11:2261-2286.
39. Yuan M., Lin Y. Model selection and estimation in the Gaussian graphical model. Biometrika 2007, 94:19-35.
40. Zahn J.M., Poosala S., Owen A., Ingram D.K., Lustig A., et al. Agemap: a gene expression database for aging in mice. PLoS Genetics 2007, 3(11):2326-2337.
41. Zhang Y., Schneider J. Learning multiple tasks with a sparse matrix-normal penalty. Advances in Neural Information Processing Systems 2010, vol. 23:2550-2558. J. Lafferty, C.K.I. Williams, J. Shawe-Taylor, R. Zemel, A. Culotta (Eds.).
42. Zou H. The adaptive lasso and its oracle properties. Journal of the American Statistical Association 2006, 101:1418-1429.