Inferring Network Structure and Estimating Dynamical Process From Binary-State Data via Logistic Regression

Qi-ming Liu, Chuang Ma, Bing-Bing Xiang, Han-Shuang Chen, Haifeng Zhang

Abstract: Inferring the structures and the dynamics of the complex networked systems based on time series data is a challenging problem. The existing reconstruction methods often rely on the knowledge of the dynamics on networks. In many cases, a prior knowledge of the dynamics is unknown, so it is natural to ask: is it possible to reconstruct network and estimate the dynamical processes on complex networks <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">only</i> rely on the observed data? In this article, we develop a framework to reconstruct the structures of networks with binary-state dynamics, in which the knowledge of the original dynamical processes is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unknown</i> . Within the reconstruction framework, the transition probabilities of binary dynamical processes are described by the Sigmoid function in logistic regression, we then apply the mean-field approximation to enable maximum likelihood estimation (MLE), which gives rise to that the network structure can be inferred by solving the linear system of equations. Meanwhile, the original dynamical processes can be simulated by estimating the parameters in the Sigmoid function. Our framework has been validated by a variety of binary dynamical processes on synthetic and empirical networks, indicating that our method can not only reveal the network structures but also estimate the dynamical processes. Moreover, the high accuracy of our method is highlighted by comparing it with the existing methods.