CaSPIAN: a causal compressive sensing algorithm for discovering directed interactions in gene networks.

We introduce a novel algorithm for inference of causal gene interactions, termed CaSPIAN (Causal Subspace Pursuit for Inference and Analysis of Networks), which is based on coupling compressive sensing and Granger causality techniques. The core of the approach is to discover sparse linear dependencies between shifted time series of gene expressions using a sequential list-version of the subspace pursuit reconstruction algorithm and to estimate the direction of gene interactions via Granger-type elimination. The method is conceptually simple and computationally efficient, and it allows for dealing with noisy measurements. Its performance as a stand-alone platform without biological side-information was tested on simulated networks, on the synthetic IRMA network in Saccharomyces cerevisiae, and on data pertaining to the human HeLa cell network and the SOS network in E. coli. The results produced by CaSPIAN are compared to the results of several related algorithms, demonstrating significant improvements in inference accuracy of documented interactions. These findings highlight the importance of Granger causality techniques for reducing the number of false-positives, as well as the influence of noise and sampling period on the accuracy of the estimates. In addition, the performance of the method was tested in conjunction with biological side information of the form of sparse "scaffold networks", to which new edges were added using available RNA-seq or microarray data. These biological priors aid in increasing the sensitivity and precision of the algorithm in the small sample regime.