Variational Bayesian Complex Network Reconstruction

The networked systems are ubiquitous in many fields, including social-tech science [1, 2], bioinformatics [3-6], epidemic dynamics [7-9] and power grid [10, 11]. However, as is often the case, it is not able to observe the topology of a network, while data generated by this network are available. Therefore, in interdisciplinary science, one of the most important but challenging problems is to reconstruct the complex network from the observed data or time series [12]. This problem has been widely investigated in the past three decades, where the classical method is the delay-coordinate embedding method proposed by Takens [13], which, nevertheless, is only suitable for small-scale networks. Nowadays, with the advent of big data era [14], it is of great urgency solve this issue for large-scale complex networks. Suppose that a complex network consists of N nodes, in practice we are often given the time series of the states for the N nodes. Generally speaking, the core idea of many data-driven network reconstruction investigations is to first calculate the correlation between two nodes. Then, a threshold can be set mutually or automatically to make the network binary.