A Full Bayesian Approach to Sparse Network Inference Using Heterogeneous Datasets

Network inference has been attracting increasing attention in several fields, notably systems biology and biomedicine. Indeed, one of our biggest challenges is to uncover and understand complex molecular networks behind cells and organisms. A network is mainly characterized by its topology and internal dynamics. In particular, sparse topologies with stable dynamics are properties present in most real-world networks. Moreover, experiments typically measure a partial set of nodes. Linear systems have been used as approximations of complex nonlinear systems in a wide range of applications. Although they exhibit simpler dynamics, they can easily model unmeasured nodes, e.g., via transfer functions, which is not possible for nonlinear systems. This article explores these properties and considers general linear network models. It develops a method, based on reversible jump Markov chain Monte Carlo, to estimate the confidence of all links and produce the most likely topology. Monte Carlo simulations indicate that our approach consistently produces more accurate networks compared with other state-of-the-art methods, including kernel-based methods, nonlinear ordinary-differential-equation-based methods (iCheMA), and machine-learning-based methods (dynGINIE3). We show that this is also true on a well-known biological nonlinear model. The proposed method can be used in a wide range of applications, such as systems biology and biomedicine, and fault detection and diagnosis