A Relational Event Approach to Modeling Behavioral Dynamics

This chapter provides an introduction to the analysis of relational event data (i.e., actions, interactions, or other events involving multiple actors that occur over time) within the R/statnet platform. We begin by reviewing the basics of relational event modeling, with an emphasis on models with piecewise constant hazards. We then discuss estimation for dyadic and more general relational event models using the relevent package, with an emphasis on hands-on applications of the methods and interpretation of results. Statnet is a collection of packages for the R statistical computing system that supports the representation, manipulation, visualization, modeling, simulation, and analysis of relational data. Statnet packages are contributed by a team of volunteer developers, and are made freely available under the GNU Public License. These packages are written for the R statistical computing environment, and can be used with any computing platform that supports R (including Windows, Linux, and Mac).

The interplay of microscopic and mesoscopic structure in complex networks

Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on unbiased generative probabilistic exponential random graph models and employing distributive message passing techniques, we present an efficient algorithm that allows one to separate the contributions of individual nodes and groups of nodes to the network structure. This leads to improved detection accuracy of latent class structure in real world data sets compared to models that focus on group structure alone. Furthermore, the inclusion of hitherto neglected group specific effects in models used to assess the statistical significance of small subgraph (motif) distributions in networks may be sufficient to explain most of the observed statistics. We show the predictive power of such generative models in forecasting putative gene-disease associations in the Online Mendelian Inheritance in Man (OMIM) database. The approach is suitable for both directed and undirected uni-partite as well as for bipartite networks

Statistical Inference for Valued-Edge Networks: Generalized Exponential Random Graph Models

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a ubiquitous means of analysis. However, they are limited by an inability to model networks with valued edges. We solve this problem by introducing a class of generalized exponential random graph models capable of modeling networks whose edges are valued, thus greatly expanding the scope of networks applied researchers can subject to statistical analysis

Dynamics and Control of Diseases in Networks with Community Structure

The dynamics of infectious diseases spread via direct person-to-person transmission (such as influenza, smallpox, HIV/AIDS, etc.) depends on the underlying host contact network. Human contact networks exhibit strong community structure. Understanding how such community structure affects epidemics may provide insights for preventing the spread of disease between communities by changing the structure of the contact network through pharmaceutical or non-pharmaceutical interventions. We use empirical and simulated networks to investigate the spread of disease in networks with community structure. We find that community structure has a major impact on disease dynamics, and we show that in networks with strong community structure, immunization interventions targeted at individuals bridging communities are more effective than those simply targeting highly connected individuals. Because the structure of relevant contact networks is generally not known, and vaccine supply is often limited, there is great need for efficient vaccination algorithms that do not require full knowledge of the network. We developed an algorithm that acts only on locally available network information and is able to quickly identify targets for successful immunization intervention. The algorithm generally outperforms existing algorithms when vaccine supply is limited, particularly in networks with strong community structure. Understanding the spread of infectious diseases and designing optimal control strategies is a major goal of public health. Social networks show marked patterns of community structure, and our results, based on empirical and simulated data, demonstrate that community structure strongly affects disease dynamics. These results have implications for the design of control strategies

Bayesian Graph Convolutional Neural Networks via Tempered MCMC

Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be represented via graphs. These types of data are often found in health and medicine, social networks, and research data repositories. Graph convolutional neural networks have recently gained attention in the field of deep learning that takes advantage of graph-based data representation with automatic feature extraction via convolutions. Given the popularity of these methods in a wide range of applications, robust uncertainty quantification is vital. This remains a challenge for large models and unstructured datasets. Bayesian inference provides a principled approach to uncertainty quantification of model parameters for deep learning models. Although Bayesian inference has been used extensively elsewhere, its application to deep learning remains limited due to the computational requirements of the Markov Chain Monte Carlo (MCMC) methods. Recent advances in parallel computing and advanced proposal schemes in MCMC sampling methods has opened the path for Bayesian deep learning. In this paper, we present Bayesian graph convolutional neural networks that employ tempered MCMC sampling with Langevin-gradient proposal distribution implemented via parallel computing. Our results show that the proposed method can provide accuracy similar to advanced optimisers while providing uncertainty quantification for key benchmark problems