Ridge estimation of the VAR(1) model and its time series chain graph from multivariate time‐course omics data

Abstract

Omics experiments endowed with a time‐course design may enable us to uncover the dynamic interplay among genes of cellular processes. Multivariate techniques (like VAR(1) models describing the temporal and contemporaneous relations among variates) that may facilitate this goal are hampered by the high‐dimensionality of the resulting data. This is resolved by the presented ridge regularized maximum likelihood estimation procedure for the VAR(1) model. Information on the absence of temporal and contemporaneous relations may be incorporated in this procedure. Its computational efficient implemention is discussed. The estimation procedure is accompanied with an LOOCV scheme to determine the associated penalty parameters. Downstream exploitation of the estimated VAR(1) model is outlined: an empirical Bayes procedure to identify the interesting temporal and contemporaneous relationships, impulse response analysis, mutual information analysis, and covariance decomposition into the (graphical) relations among variates. In a simulation study the presented ridge estimation procedure outperformed a sparse competitor in terms of Frobenius loss of the estimates, while their selection properties are on par. The proposed machinery is illustrated in the reconstruction of the p53 signaling pathway during HPV‐induced cellular transformation. The methodology is implemented in the ragt2ridges R‐package available from CRAN.