A Novel Method for Estimating Accuracy of Network Structure Recovery Model

Abstract

Many practical systems can be considered as networks of nodes interacting. Explicit network topology is a straightforward method to understand the actual system, so it is of practical significance to obtain the complete network topology from the empirically measured time series. With the premise that the dynamics equations and coupling matrix are known, a method to reconstruct the network topology from the measured time series is proposed, and based on regression theory the estimated matrix form of the adjacency matrix is given. Also, the method is suitable for predicting arbitrary weights of network connections, and its practicality is verified by numerical simulations. Importantly for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0-1$ </tex-math></inline-formula> matrix, a new method for judging the prediction performance of the model using the false negative rate is proposed. It can estimate the accuracy of model prediction with only partial sampling data when the information of network topology is unknown. In addition, a method that can control false positives is proposed, and the feasibility of the method is verified by numerical simulation. Finally, two factors that affect model performance, the amount of sample data and the intensity of noise, are discussed.