Structured learning of time-varying networks with application to PM2.5 data

In this paper, we study the problem of estimating structured time-varying networks from time-dependent observational data. In the penalized log-likelihood framework, we exploit a fused lasso-based penalty to encourage the networks of neighboring time stamps having similar structure patterns. Further, edges between two distinct communities are penalized more than those within one common community to capture the community structure of networks. We use the alternating direction method of multipliers to solve the problem followed by a series of simulations. Finally, we apply the method to learn the network structure among 31 Chinese cities and obtain interpretable results.