Updating of the Gaussian graphical model through targeted penalized estimation

Updating of the Gaussian graphical model via shrinkage estimation is studied. This shrinkage is towards a nonzero parameter value representing prior quantitative information. Once new data become available, the previously estimated parameter needs updating. Shrinkage provides the means to this end, using the latter as a shrinkage target to acquire an updated estimate. The process of iteratively updating the Gaussian graphical model in shrinkage fashion is shown to yield an improved fit and an asymptotically unbiased and consistent estimator. The workings of updating via shrinkage are elucidated by linking it to Bayesian updating and through the inheritance by the update of eigen-properties of the previous estimate. The effect of shrinkage on the moments and loss of the estimator are pointed out. Practical issues possibly hampering updating are identified and solutions outlined. The presented updating procedure is illustrated through the reconstruction of a gene–gene interaction network using transcriptomic data.