Bayesian Inference of Stochastic Dynamical Networks

Network inference has been extensively studied in several fields, such as systems biology and social sciences. Learning network topology and internal dynamics is essential to understand mechanisms of complex systems. In particular, sparse topologies and stable dynamics are fundamental features of many real-world continuous-time networks. Given that usually only a partial set of nodes are able to observe, in this paper, we consider linear continuous-time systems to depict networks since they can model unmeasured nodes via transfer functions. Additionally, measurements tend to be noisy and with low and varying sampling frequencies. For this reason, we consider continuous-time models (CT) since discrete-time approximations often require fine-grained measurements and uniform sampling steps. The developed method applies dynamical structure functions (DSFs) derived from linear stochastic differential equations (SDEs) to describe networks of measured nodes. Further, a numerical sampling method, preconditioned Crank-Nicolson (pCN), is used to refine coarse-grained trajectories to improve inference accuracy. The simulation conducted on random and ring networks, and a synthetic biological network illustrate that our method achieves state-of-the-art performance compared with group sparse Bayesian learning (GSBL), BINGO, kernel-based methods, dynGENIE3, GENIE3 and ARNI. In particular, these are challenging networks, suggesting that the developed method can be applied under a wide range of contexts.