Structured learning of time-varying networks with application to PM_2.5 data

Abstract

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 ${\text{PM}}_{2.5}$ network structure among 31 Chinese cities and obtain interpretable results.

Keywords:

• Graphical model
• Dynamic network
• Community structure
• ADMM
• ${\text{PM}}_{2.5}$

Notes

1 https://www.aqistudy.cn/

Additional information

Funding

This work was partially supported by National Natural Science Foundation of China under grant numbers 11571011 and U1811461.