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Inferring Dynamic Genetic Networks with Low Order Independencies

Author

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  • Lèbre Sophie

    (Université d’Evry-Val-D’Essonne, Laboratoire Statistique et Genome (UMR CNRS 8071))

Abstract

In this paper, we introduce a novel inference method for dynamic genetic networks which makes it possible to face a number of time measurements n that is much smaller than the number of genes p. The approach is based on the concept of a low order conditional dependence graph that we extend here in the case of dynamic Bayesian networks. Most of our results are based on the theory of graphical models associated with the directed acyclic graphs (DAGs). In this way, we define a minimal DAG G which describes exactly the full order conditional dependencies given in the past of the process. Then, to face with the large p and small n estimation case, we propose to approximate DAG G by considering low order conditional independencies. We introduce partial qth order conditional dependence DAGs G(q) and analyze their probabilistic properties. In general, DAGs G(q) differ from DAG G but still reflect relevant dependence facts for sparse networks such as genetic networks. By using this approximation, we set out a non-Bayesian inference method and demonstrate the effectiveness of this approach on both simulated and real data analysis. The inference procedure is implemented in the R package 'G1DBN' freely available from the R archive (CRAN).

Suggested Citation

  • Lèbre Sophie, 2009. "Inferring Dynamic Genetic Networks with Low Order Independencies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-40, February.
    • Handle: RePEc:bpj:sagmbi:v:8:y:2009:i:1:n:9
    DOI: 10.2202/1544-6115.1294
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    References listed on IDEAS

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    1. 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.
    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.
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