Uncertainty propagation in shrinkage-based partial correlations

Gaussian graphical models (GGMs) are network models where random
variables are represented by nodes and their pair-wise partial correlation by
edges. The inference of a GGM demands the estimation of the precision matrix
(i.e. the inverse of the covariance matrix); however, this becomes problematic
when the number of variables is larger than the sample size. Covariance estimators based on shrinkage (a type of regularization) overcome these pitfalls and result in a ’shrunk’ version of the GGM. Traditionally, shrinkage is justified at model level (as a regularized covariance). In this work, we re-interpret the shrinkage from a data level perspective (as a regularized data). Our result allows the propagation of uncertainty from the data into the GGM structure.