Statistical Inference of Large-scale Structure in Networks

Abstract

Networks are flexible representations of systems governed by many interacting components. This flexibility has led to their application across a broad range of disciplines, modeling trade between countries, cascading failures in power grids, the structure of the World Wide Web, neuronal connections in microscopic organisms like C. elegans, and even human and animal social dynamics. Crucially, networks capture the patterns of interactions between the components of a system. The structured nature of networks can be used to better understand the underlying dynamics of the system. In this thesis, we develop theoretical models to reveal large-scale structures in networks and explore how network structures can be used to make predictions.

We begin with a basic overview of how networks and network tools have been used to study scientific systems. Then, we motivate the use of networks by constructing a novel network of drugs and the diseases they treat. To this network, we apply network models for link prediction to address questions related to drug repurposing. Link prediction aims to estimate those edges that may be missing from the network, the prediction of which could motivate the study of potential candidates for drug repurposing. Previous work on network-based drug repurposing has focused primarily on networks of indirect connections between drugs and diseases, such as drug-protein or drug-gene networks. Some work has been done on drug-disease interactions, but using networks much smaller in scope. We do extensive cross-validation tests and discuss bounds on how well these link prediction methods can do on our dataset.

We then turn our focus to the modeling of large-scale structures in networks. First, we consider core-periphery structure, a structure commonly found in many types of network. Often times, this structure is considered with only two groups: a core and a periphery. This partition of the network is related to the importance or centrality of nodes, with more central nodes being in the core. There has been substantial research on models for networks characterized by this structure, and we extend these works by proposing one that can reveal more flexible divisions network. Crucially, we allow for multiple cores and peripheries, but also more general hierarchical structures. We propose a generative model that allows for any number of groups along with a model-fitting approach to determine the number of groups directly from the network data.

Second, we study community structure in higher-order networks. With the growing popularity of higher-order networks, there is increasing interest in extending established methods for treating dyadic networks to these more complex ones. Detecting communities in higher-order networks could potentially reveal more sophisticated social structures in social networks or nontrivial functions of components in neuronal networks. We propose a generative model for community structure in higher-order networks and evaluate its performance on a representative selection of empirically measured networks with ground truth community structure.

These works collectively use network structure to provide insight into real-world network data and contribute additional tools for researchers to study their network systems.