Structured Regression on Multilayer Networks

Until recently, research in social network analysis was focused on single layer networks, where only one type of links among nodes is considered. This approach does not consider the variety of interactions that exist among nodes, resulting in the loss of a large amount of information. In the last few years there is an advanced interest in multilayer networks analysis, where multiple types of nodal connections are considered jointly. In most approaches however the contributions of the various interactions are averaged, resulting again in the loss of information. In this work we present a structured regression model for node attribute prediction in multilayer networks. Our Gaussian Conditional Random Fields model is designed to maximize the information gained from the use of data with multiple layers of graphical structure. Our model accommodates graphs with layers that share the same set of nodes allowing for missing nodes and unobserved connections. At the same time it models the evolution of such networks over time without requiring the addition of a new layer. We present evidence that this model outperforms the traditionally used one and that it offers predictive accuracy that increases as the number of layers used grows, on both synthetic data and challenging real world applications such as predicting citation count and sepsis hospitalization admission rate at all hospitals in California.