Dynamic Structure Estimation of Time-Varying Networks

Abstract

Complex networks, such as biological networks and social networks, typically change over time. However, most of the existing methods of network analysis assume a static structure of this network, which is not realistic. In this project, we allow the links between the nodes in a network to change over time and propose a general framework for modeling and estimating the dynamic links of time-varying networks. In particular, by accounting for correlations among the networks over time, we develop a new penalized regression method to estimate the dynamical links and detect changes in the network structure. Towards this, we generalize the autoregressive model from time series data analysis to time-varying networks and employ the sparsity estimation tool via fused lasso to identify jumps for the node links. Compared with existing network models, the proposed method can not only explain the dependencies between nodes at a given time point but also capture the structural changes of the network over time. To implement the proposed method, we develop an efficient alternating direction method of multipliers (ADMM) algorithm and use the Akaike information criterion (AIC) and Bayesian information criterion (BIC), and the cross-validation (CV) errors to select the best model. Numerical experiments are carried out to evaluate the proposed method and compare it with existing methods. The proposed method offers an effective tool for analyzing a sequence of networks that change over time, which are commonly encountered in real-world problems. In particular, to demonstrate its empirical performance, we apply the proposed method to analyze a real ecological network data set and gain insight into changes in relations over time among the species in an ecological network.