Optimal Sparsity Criteria for Network Inference

Abstract Gene regulatory network inference (that is, determination of the regulatory interactions between a set of genes) provides mechanistic insights of central importance to research in systems biology. Most contemporary network inference methods rely on a sparsity/regularization coefficient, which we call ζ (zeta), to determine the degree of sparsity of the network estimates, that is, the total number of links between the nodes. However, they offer little or no advice on how to select this sparsity coefficient, in particular, for biological data with few samples. We show that an empty network is more accurate than estimates obtained for a poor choice of ζ. In order to avoid such poor choices, we propose a method for optimization of ζ, which maximizes the accuracy of the inferred network for any sparsity-dependent inference method and data set. Our procedure is based on leave-one-out cross-optimization and selection of the ζ value that minimizes the prediction error. We also illustrate the adverse effe...