Detecting network structures from measurable data produced by dynamics with hidden variables.

Depicting network structures from measurable data is of significance. In real-world situations, it is common that some variables of networks are unavailable or even unknown. These unavailable and unknown variables, i.e., hidden variables, will lead to much reconstruction error, even make reconstruction methods useless. In this paper, to solve hidden variable problems, we propose three reconstruction methods, respectively, based on the following conditions: statistical characteristics of hidden variables, linearizable hidden variables, and white noise injection. Among them, the method based on white noise injection is active and invasive. In our framework, theoretic analyses of these three methods are given at first, and, furthermore, the validity of theoretical derivations and the robustness of these methods are fully verified through numerical results. Our work may be, therefore, helpful for practical experiments.