Model-Based Clustering of Nonparametric Weighted Networks With Application to Water Pollution Analysis

Abstract

Water pollution is a major global environmental problem, and it poses a great environmental risk to public health and biological diversity. This work is motivated by assessing the potential environmental threat of coal mining through increased sulfate concentrations in river networks, which do not belong to any simple parametric distribution. However, existing network models mainly focus on binary or discrete networks and weighted networks with known parametric weight distributions. We propose a principled nonparametric weighted network model based on exponential-family random graph models and local likelihood estimation, and study its model-based clustering with application to large-scale water pollution network analysis. We do not require any parametric distribution assumption on network weights. The proposed method greatly extends the methodology and applicability of statistical network models. Furthermore, it is scalable to large and complex networks in large-scale environmental studies. The power of our proposed methods is demonstrated in simulation studies and a real application to sulfate pollution network analysis in Ohio watershed located in Pennsylvania, United States.

Keywords:

• Environmental studies
• Exponential-family random graphical model
• Local likelihood
• Variational inference

Acknowledgments

The authors thank the editor, an associate editor, and two referees for their constructive comments and suggestions. Amal Agarwal and Lingzhou Xue have been partially supported by the National Institute on Drug Abuse grant P50DA039838 and the National Science Foundation grants DMS-1505256 and DMS-1811552.

Additional information

Funding

Amal Agarwal and Lingzhou Xue have been partially supported by the National Institute on Drug Abuse grant P50DA039838 and the National Science Foundation grants DMS-1505256 and DMS-1811552