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This article is part of the supplement: Probabilistic Modeling and Machine Learning in Structural and Systems Biology

Open Access Open Badges Research

Learning causal networks from systems biology time course data: an effective model selection procedure for the vector autoregressive process

Rainer Opgen-Rhein1* and Korbinian Strimmer2

Author Affiliations

1 Department of Statistics, Ludwig-Maximilians-Universität München, Ludwigstraße 33, D-80539 München, Germany

2 Institute for Medical Informatics, Statistics and Epidemiology (IMISE), University of Leipzig, Härtelstr. 16-18, 04107 Leipzig, Germany

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BMC Bioinformatics 2007, 8(Suppl 2):S3  doi:10.1186/1471-2105-8-S2-S3

Published: 3 May 2007



Causal networks based on the vector autoregressive (VAR) process are a promising statistical tool for modeling regulatory interactions in a cell. However, learning these networks is challenging due to the low sample size and high dimensionality of genomic data.


We present a novel and highly efficient approach to estimate a VAR network. This proceeds in two steps: (i) improved estimation of VAR regression coefficients using an analytic shrinkage approach, and (ii) subsequent model selection by testing the associated partial correlations. In simulations this approach outperformed for small sample size all other considered approaches in terms of true discovery rate (number of correctly identified edges relative to the significant edges). Moreover, the analysis of expression time series data from Arabidopsis thaliana resulted in a biologically sensible network.


Statistical learning of large-scale VAR causal models can be done efficiently by the proposed procedure, even in the difficult data situations prevalent in genomics and proteomics.


The method is implemented in R code that is available from the authors on request.