Fitting very large sparse Gaussian graphical models

Computational Statistics and Data Analysis

Volumn 56, Issue 9, 2012, Pages 2626-2636

  Kiiveri, Harri ^a   De Hoog, Frank ^a  

^a CSIRO   (Australia)

Author keywords

Covariance selection; Gene networks; Graphical models; High dimensional; Large scale optimisation; Limited memory quasi Newton

Indexed keywords

COVARIANCE SELECTION; GENE NETWORKS; GRAPHICAL MODEL; HIGH-DIMENSIONAL; OPTIMISATIONS; QUASI-NEWTON;

ALGORITHMS; GENES; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; NEWTON-RAPHSON METHOD; OPTIMIZATION;

GRAPHIC METHODS;

EID: 84859916745     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2012.02.007     Document Type: Article

References (43)

1. An, H.; Huang, D.; Yao, Q.; Zhang, C.; 2008. Stepwise searching for feature variables in high-dimensional linear regression. Available at: http://stats.lse.ac.uk/q.yao/qyao.links/paper/ahyz08.pdf.
2. O. Banerjee, L. Ghaoui, and A. D'aspremont Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data Journal of Machine Learning Research 9 2008 485 516
3. O. Barndorff-Nielsen Information and Exponential Families in Statistical Theory 1978 Wiley New York
4. S. Buhl On the existence of maximum-likelihood estimators for graphical Gaussian models Scandinavian Journal of Statistics 20 1993 263 270
5. Campbell, Y.E.; Davis, T.A.; 1995a. Computing the sparse inverse subset: an inverse multifrontal approach. Technical Report REP-1995-183. University of Florida.
6. Campbell, Y.E.; Davis, T.A.; 1995b. Parallel implementation of the block-partitioned inverse multifrontal Zsparse algorithm. Technical Report, REP-1995-184. University of Florida.
7. J. Chen, and Z. Chen Extended Bayesian information criteria for model selection with large model spaces Biometrika 95 3 2008 759 771
8. J. Dahl, L. Vandenberghe, and V. Roychowdhury Covariance selection for nonchordal graphs via chordal embedding Optimization Methods and Software 23 2008 501 520
9. F.R. de Hoog, R.S. Anderssen, and M.A. Lukas Differentiation of matrix functionals using triangular factorization Mathematics of Computation 80 275 2011 1585 1600
10. A. Dempster Covariance selection Biometrics 28 1972 157 175
11. J.E. Dennis, and J.J. Moré Quasi-Newton methods, motivation and theory SIAM Review 19 1977 46 89
12. I.S. Duff, A.M. Erisman, and J.K. Reid Direct Methods for Sparse Matrices 1989 Oxford University Press USA
13. B. Efron, T. Hastie, I. Johnston, and R. Tibshirani Least angle regression (with discussion) Annals of Mathematical Statistics 32 2 2004 407 499
14. A.M. Erisman, and W.F. Tinney On computing certain elements of the inverse of a sparse matrix Communications of the ACM 18 1975 177 179
15. J. Fan, and R. Li Variable selection via nonconcave penalized likelihood and its oracle properties Journal of the American Statistical Association 96 456 2001 1348 1360
16. R. Fletcher, and C.M. Reeves Function minimization by conjugate gradients The Computer Journal 7 1964 148 154
17. J. Friedman, T. Hastie, and R. Tibshirani Sparse inverse covariance estimation with the lasso Biostatistics 9 2008 432 441
18. J. Friedman, T. Hastie, and R. Tibshirani Regularization paths for generalized linear models via coordinate descent Journal of Statistical Software 33 1 2008 1 22
19. George, A.; Liu, J.W.; 1981. Computer Solution of Large Sparse Positive Definite Systems, in: Prentice Hall Series in Computational Mathematics, NJ.
20. G.H. Golub, and C.F. Van Loan Matrix Computations third ed. 1996 The Johns Hopkins University Press
21. H.V. Henderson, and S.R. Searle Vec and vech operators for matrices, with some uses in Jacobians and multivariate statistics Canadian Journal of Statistics 7 1979 65 81
22. M.R. Hestenes, and E. Stiefel Methods of conjugate gradients for solving linear systems Journal of Research of the National Bureau of Standards 49 1952 409 436
23. S. Højsgaard, and S.L. Lauritzen Graphical Gaussian models with edge and vertex symmetries Journal of the Royal Statistical Society: Series B 70 2008 1005 1027
24. G. Karypis, and V. Kumar A fast and highly quality multilevel scheme for partitioning irregular graphs SIAM Journal on Scientific Computing 20 1999 359 392
25. H.T. Kiiveri Multivariate analysis of microarray data: differential expression and differential connection BMC Bioinformatics 12 1 2011 42
26. S.L. Lauritzen Graphical Models 1996 Oxford University Press USA
27. D. Liu, and J. Nocedal On the limited memory BFGS method for large scale optimization Mathematical Programming B 45 1989 503 528
28. N. Meinshausen, and P. Bhlmann High-dimensional graphs and variable selection with the Lasso Annals of Statistics 34 2006 1436 1462
29. S.G. Nash A survey of truncated-Newton methods Journal of Computational and Applied Mathematics 124 2000 45 59
30. Niskanen, S.; stergrd, P.R.J.; 2003. Cliquer user's guide, Version 1.0.; Tech. Rep. T48.; Communications Laboratory, Helsinki University of Technology, Espoo, Finland.
31. J. Nocedal Updating quasi-Newton matrices with limited storage Mathematics of Computation 35 1980 773 782
32. Nocedal, J.; 1990. L-BFGS software for large-scale unconstrained optimization. Available at: http://users.eecs.northwestern.edu/~nocedal/lbfgs. html.
33. R.C. Read Graph Theory and Computing 1972 Academic Press New York
34. D.J. Rose Triangulated graphs and the elimination process Journal of Mathematical Analysis and its Applications 32 1970 597 609
35. Shahnaz, R.; Usman, A.; Chughtai, I.R.; 2005. Review of storage techniques for sparse matrices. In: 9th International Multitopic Conference, IEEE INMIC 2005.
36. G.K. Smyth Linear models and empirical Bayes methods for assessing differential expression in microarray experiments Statistical Applications in Genetics and Molecular Biology 3 1 2004 Article 3
37. T.P. Speed, and H.T. Kiiveri Gaussian Markov distributions over finite graphs The Annals of Statistics 14 1986 138 150
38. A. Spira, J. Beane, V. Shah, G. Liu, F. Schembri, X. Yang, J. Palma, and J. Brody Effects of cigarette smoke on the human airway epithelial cell transcriptome Proceedings of the National Academy of Sciences 101 27 2004 10143 10148
39. Spira, A.; Beane, J.; Shah, V.; Liu, G.; Schembri, F.; Yang, X.; Palma, J.; Brody, J.; 2004b. Raw data files available at: http://www.ncbi.nlm.nih.gov/ geo/query/acc.cgi?acc=GSE994.
40. Takahashi, K.; Fagan, J.; Mo-shing, C.; 1973. Formation of a sparse bus impedance matrix and its application to short circuit study. In: 8th PICA Conference Proceedings, Minneapolis.
41. R. Tibshirani Regression shrinkage and selection via the Lasso Journal of the Royal Statistical Society Series B: Methodological 58 1 1996 267 288
42. N. Wermuth Linear recursive equations, covariance selection and path analysis Journal of the American Statistical Association 75 1980 963 972
43. T. Zhang On the consistency of feature selection using greedy least squares regression Journal of Machine Learning Research 10 2009 555 568