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

Background: 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. Results: 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. Conclusion: 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. Availability: The method is implemented in R code that is available from the authors on request.