Advancements in latent space network modelling

Turnbull, Kathryn and Nemeth, Christopher and Lunagomez Coria, Simon and Nunes, Matthew (2020) Advancements in latent space network modelling. PhD thesis, Lancaster University.

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Abstract

The ubiquity of relational data has motivated an extensive literature on network analysis, and over the last two decades the latent space approach has become a popular network modelling framework. In this approach, the nodes of a network are represented in a low-dimensional latent space and the probability of interactions occurring are modelled as a function of the associated latent coordinates. This thesis focuses on computational and modelling aspects of the latent space approach, and we present two main contributions. First, we consider estimation of temporally evolving latent space networks in which interactions among a fixed population are observed through time. The latent coordinates of each node evolve other time and this presents a natural setting for the application of sequential monte carlo (SMC) methods. This facilitates online inference which allows estimation for dynamic networks in which the number of observations in time is large. Since the performance of SMC methods degrades as the dimension of the latent state space increases, we explore the high-dimensional SMC literature to allow estimation of networks with a larger number of nodes. Second, we develop a latent space model for network data in which the interactions occur between sets of the population and, as a motivating example, we consider a coauthorship network in which it is typical for more than two authors to contribute to an article. This type of data can be represented as a hypergraph, and we extend the latent space framework to this setting. Modelling the nodes in a latent space provides a convenient visualisation of the data and allows properties to be imposed on the hypergraph relationships. We develop a parsimonious model with a computationally convenient likelihood. Furthermore, we theoretically consider the properties of the degree distribution of our model and further explore its properties via simulation.