On the application of Bayesian inference to network estimation problems

Abstract

Interconnected network structures play a crucial role in many aspects of our lives. Understanding these networks and the dynamic processes that can propagate over them gives rise to many interesting questions. While many network and dynamical models are probabilistic, many of the current methods to solve key network science problems do not account for the uncertainties in the systems. In this thesis we look at networks in a probabilistic setting and use Bayesian methods to simulate from distributions of these networks to address key network science problems. This allows deeper understanding about the system of interest and allows us to quantify uncertainty for improved decision making. Specifically, in Chapters 3 and 4 we develop an algorithm that simulates connected random networks and explore how variations to the algorithm can improve performance of sampling the high dimensional posterior. This develops techniques that we further apply in Chapters 5 and 6 to an interesting inverse problem in social network analysis - the ‘Network Inference problem’. The underlying premise is to infer network structure, how people are connected, when we can only observe things moving between actors in the social network, e.g., tweets of news articles. By using a Bayesian method we can provide uncertainty estimates for the inferences we make. We consider a variety of methods to extend the applicability to a wide range of data types, including streaming data, and test the inference on both simulated and real data. Finally, in Chapter 7, we consider the ‘Network Tomography problem’, which aims to infer node properties when we only have information about paths in the network. We highlight the benefits of Bayesian inference methods in two specific applications to aid decision making when identifying routing policies over the internet. Throughout this work we highlight that applying Bayesian inference techniques to novel applications in network science can expand the types of networks we can simulate, provide uncertainty quantification for making informed decisions and gain results and insight in low and messy data regimes.