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

Rainer Opgen-Rhein,Korbinian Strimmer

doi:10.1186/1471-2105-8-s2-s3

Rainer Opgen-Rhein, Korbinian Strimmer

Open Access

https://doi.org/10.1186/1471-2105-8-s2-s3

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Abstract

BackgroundCausal 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.ResultsWe 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.ConclusionStatistical 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.AvailabilityThe method is implemented in R code that is available from the authors on request.

Highlights

Causal networks based on the vector autoregressive (VAR) process are a promising statistical tool for modeling regulatory interactions in a cell
Simulation study In a comparative simulation study we investigated the power of diverse approaches to recovering the true VAR network
In addition to the shrinkage procedure we estimated regression coefficients by ordinary least squares (OLS) and by ridge regression (RR). All these three regression strategies were applied in conjunction with the above VAR model selection based on partial correlations, with a cutoff value for the "local fdr" statistic set at 0.2 – the recommendation of [11]

Summary

Introduction

Causal networks based on the vector autoregressive (VAR) process are a promising statistical tool for modeling regulatory interactions in a cell. Learning these networks is challenging due to the low sample size and high dimensionality of genomic data. BMC Bioinformatics 2007, 8(Suppl 2):S3 http://www.biomedcentral.com/1471-2105/8/S2/S3 for learning causal VAR networks from time course data with only a few time points, and no or little replication. This procedure is based on regularized estimation of VAR coefficients, followed by subsequent simultaneous significance testing of the corresponding partial correlation coefficients

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Conclusion