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Assessing the Validity Domains of Graphical Gaussian Models in Order to Infer Relationships among Components of Complex Biological Systems

Author

Listed:
  • Villers Fanny

    (INRA Jouy-En-Josas)

  • Schaeffer Brigitte

    (INRA Jouy-En-Josas)

  • Bertin Caroline

    (INRA Jouy-En-Josas)

  • Huet Sylvie

    (INRA Jouy-En-Josas)

Abstract

The study of the interactions of cellular components is an essential base step to understand the structure and dynamics of biological networks. Various methods were recently developed for this purpose. While most of them combine different types of data and a priori knowledge, methods based on graphical Gaussian models are capable of learning the network directly from raw data. They consider the full-order partial correlations which are partial correlations between two variables given the remaining ones, for modeling direct links between variables. Statistical methods were developed for estimating these links when the number of observations is larger than the number of variables. However, the rapid advance of new technologies that allow the simultaneous measure of genome expression, led to large-scale datasets where the number of variables is far larger than the number of observations. To get around this dimensionality problem, different strategies and new statistical methods were proposed. In this study we focused on statistical methods recently published. All are based on the fact that the number of direct relationships between two variables is very small in regards to the number of possible relationships, p(p-1)/2. In the biological context, this assumption is not always satisfied over the whole graph. It is essential to precisely know the behavior of the methods in regards to the characteristics of the studied object before applying them. For this purpose, we evaluated the validity domain of each method from wide-ranging simulated datasets. We then illustrated our results using recently published biological data.

Suggested Citation

  • Villers Fanny & Schaeffer Brigitte & Bertin Caroline & Huet Sylvie, 2008. "Assessing the Validity Domains of Graphical Gaussian Models in Order to Infer Relationships among Components of Complex Biological Systems," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(2), pages 1-37, September.
    • Handle: RePEc:bpj:sagmbi:v:7:y:2008:i:2:n:14
    DOI: 10.2202/1544-6115.1371
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    References listed on IDEAS

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    1. Werhli Adriano V & Husmeier Dirk, 2007. "Reconstructing Gene Regulatory Networks with Bayesian Networks by Combining Expression Data with Multiple Sources of Prior Knowledge," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-47, May.
    2. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    3. Wille Anja & Bühlmann Peter, 2006. "Low-Order Conditional Independence Graphs for Inferring Genetic Networks," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-34, January.
    4. Alberto Roverato & Robert Castelo, 2006. "Structural learning of Gaussian graphical models from microarray data with p larger than n," Statistica, Department of Statistics, University of Bologna, vol. 66(4), pages 343-372.
    5. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    6. Dobra, Adrian & Hans, Chris & Jones, Beatrix & Nevins, J.R.Joseph R. & Yao, Guang & West, Mike, 2004. "Sparse graphical models for exploring gene expression data," Journal of Multivariate Analysis, Elsevier, vol. 90(1), pages 196-212, July.
    7. Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
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