A robust procedure for Gaussian graphical model search from microarray data with p larger than n

Journal of Machine Learning Research

Volumn 7, Issue , 2006, Pages 2621-2650

  Castelo, Robert ^a   Roverato, Alberto ^b  

^a UNIVERSITAT POMPEU FABRA   (Spain)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Gaussian distribution; Gene network; Graphical model; Microarray data; Non rejection rate; Partial correlation; Small sample inference

Indexed keywords

CORRELATION METHODS; DATA REDUCTION; LEARNING SYSTEMS; MATHEMATICAL MODELS; PROBLEM SOLVING;

GAUSSIAN DISTRIBUTION; GENE NETWORK; GRAPHICAL MODELS; MICROARRAY DATA; NON REJECTION RATE; PARTIAL CORRELATION; SMALL SAMPLE INFERENCE;

GRAPHIC METHODS;

EID: 33845523872     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. A.J. Butte, P. Tamayo, D. Slonim, T.R. Golub and I.S. Kohane. Discovering functional relationships between RNA expression and chemotherapeutic susceptibility using relevance networks. Proceedings of the National Academy of Sciences, 97(22): 12182-12186, 2000.
2. R.G. Cowell, A.P. Dawid, S.L. Lauritzen and D.J. Spiegelhalter. Probabilistic networks and expert systems. Springer-Verlag, New York, 1999.
3. D.R. Cox and N. Wermuth. Linear dependencies represented by chain graphs (with discussion). Statist. Sci., 8: 204-283, 1993.
4. D.R. Cox and N. Wermuth. Multivariate dependencies: Models, analysis and interpretation. Chapman and Hall, London, 1996.
5. A. de la Fuente, N. Bing, I. Hoeschele and P. Mendes. Discovery of meaningful associations in genomic data using partial correlation coefficients. Bioinformatics, 20: 3565-3574, 2004.
6. A.P. Dempster. Elements of continuous multivariate analysis. Addison-Wesley, Reading, Massachusetts, 1969.
7. A.P. Dempster. Covariance selection. Biometrics, 28: 157-75, 1972.
8. R. Diestel. (2005). Graph theory. Springer-Verlag, Heidelberg, 2005.
9. A. Dobra, C. Hans, B. Jones, J.R. Nevins and M. West. Sparse graphical models for exploring gene expression data. J. Mult. Anal. 90: 196-212, 2004.
10. M. Drton and M.D. Perlman. Model selection for Gaussian concentration graphs. Biometrika, 91(3): 591-602, 2004.
11. M. Drton and T. Richardson. Iterative conditional fitting for estimation of a covariance matrix with zeros. Technical Report no. 469, Department of Statistics, University of Washington, 2004.
12. R.L. Dykstra. Establishing the positive definiteness of the sample covariance matrix. Ann. Math. Statist., 41(6): 2153-2154, 1970.
13. D.E. Edwards. Introduction to graphical modelling. Springer-Verlag, New York, 2000.
14. N. Friedman. Inferring cellular network using probabilistic graphical models. Science, 33: 799-805, 2004.
15. B. Jones, A. Dobra, C. Carvalho, C. Hans, C. Carter and M. West. Experiments in stochastic computation for high-dimensional graphical models. Statistical Science, 20(4): 388-400, 2005.
16. B. Jones and M. West. Covariance decomposition in undirected Gaussian graphical models. Biometrika, 92(4): 779-786, 2005.
17. S.L. Lauritzen. Graphical models. Oxford University Press, Oxford, 1996.
18. E.L. Lehmann. Testing statistical hypotheses, 2nd edition. Wiley, New York, 1986.
19. P.M. Magwene and J. Kim. Estimating genomic coexpression networks using first-order conditional independence. Genome Biology, 5: R100, 2004.
20. A.A. Margolin, I. Nemenman, K. Basso, C. Wiggins, G. Stolovitzky, R.D. Favera and A. Califano. ARACNE: an algorithm for the reconstruction of gene regulatory networks ina mammalian cellular context. BMC Bioinformatics, 7(Suppl 1):S7, 2006.
21. R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii and U. Alon. Network motifs: simple building blocks of complex networks. Science, 298: 824-827, 2002.
22. J. Pearl. Probabilistic reasoning in intelligent systems. Morgan Kaufmann, San Mateo, 1988.
23. A.L. Rosenberg and L.S. Heath. Graph separators, with applications. Kluwer Academic Publishers, New York, 2001.
24. A. Roverato. Hyper inverse Wishart distribution for non-decomposable graphs and its application to Bayesian inference for Gaussian graphical models. Scand. J. Statist., 29: 391-411, 2002.
25. J. Schäfer and K. Strimmer. An empirical Bayes approach to inferring large-scale gene association networks. Bioinformatics, 21(6): 754-764, 2005a.
26. J. Schäfer and K. Strimmer. Learning large-scale graphical Gaussian models from genomic data. In: J.F. Mendes. (Ed.). Proceeding of Science of Complex Networks: from Biology to the Internet and WWW (CNET 2004), Aveiro, PT, (Publisher: The American Institute of Physics), 2005b.
27. J. Schäfer and K. Strimmer. A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4(1): article 32, 2005c.
28. R. Steuer, J. Kurths, O. Fiehn and W. Weckwerth. Interpreting correlations in metabolomic networks. Bioch. Soc. Trans., 31: 1476-1478, 2003a.
29. R. Steuer, J. Kurths, O. Fiehn and W. Weckwerth. Observing and interpreting correlations in metabolomic networks. Bioinformatics, 19: 1019-1026, 2003b.
30. M. West, C. Blanchette, H. Dressman, E. Huang, S. Ishida, R. Spang, H. Zuzan, J.A. Olson, J.R. Marks and J.R. Nevings. Predicting the clinical status of human breast cancer by using gene expression profiles. Proceedings of the National Academy of Sciences, 98(20): 11462-11467, 2001.
31. A. Wille and P. Bühlmann. Low-order conditional independence graphs for inferring genetic networks. Statistical Applications in Genetics and Molecular Biology, 5(1): article 1, 2006.
32. A. Wille, P. Zimmermann, E. Vranová, A. Fürholz, O. Laule, S. Bleuler, L. Hennig, A. Prelić, P. von Rohr, L. Thiele, E. Zitzler, W. Gruissem and P. Bühlmann. Sparse graphical Gaussian modeling of the isoprenoid gene network in Arabidopsis thaliana. Genome Biology, 5:R92, 2004.
33. E. Wit and J. McClure. Statistics for microarrays. Design, analysis and inference. Wiley, Chichester, 2004.
34. J. Whittaker. Graphical models in applied multivariate statistics. Wiley, Chichester, 1990.
35. F. Wong, C.K. Carter and R. Kohn. Efficient estimation of covariance selection models. Biometrika, 90: 809-830, 2003.
36. R. Yang, and J.O. Berger. Estimation of a covariance matrix using the reference priors. Ann. Statist., 3: 1195-1211, 1994.
37. E. Yeger-Lotem, S. Sattath, N. Kashtan, S. Itzkovitz, R. Milo, R.Y. Pinter, U. Alon and H. Margalit. Network motifs in integrated cellular networks of transcription-regulation and protein-protein interaction. Proc. Natl. Acad. Sci., 101(16): 5934-5939, 2004.