Stability in GRN inference

Reconstructing a gene regulatory network from one or more sets of omics measurements has been a major task of computational biology in the last twenty years. Despite an overwhelming number of algorithms proposed to solve the network inference problem either in the general scenario or in a ad-hoc tailored situation, assessing the stability of reconstruction is still an uncharted territory and exploratory studies mainly tackled theoretical aspects. We introduce here empirical stability, which is induced by variability of reconstruction as a function of data subsampling. By evaluating differences between networks that are inferred using different subsets of the same data we obtain quantitative indicators of the robustness of the algorithm, of the noise level affecting the data, and, overall, of the reliability of the reconstructed graph. We show that empirical stability can be used whenever no ground truth is available to compute a direct measure of the similarity between the inferred structure and the true network. The main ingredient here is a suite of indicators, called NetSI, providing statistics of distances between graphs generated by a given algorithm fed with different data subsets, where the chosen metric is the Hamming-Ipsen-Mikhailov (HIM) distance evaluating dissimilarity of graph topologies with shared nodes. Operatively, the NetSI family is demonstrated here on synthetic and high-throughput datasets, inferring graphs at different resolution levels (topology, direction, weight), showing how the stability indicators can be effectively used for the quantitative comparison of the stability of different reconstruction algorithms.