Advancements in latent space network modelling

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

A State-Space Model for the Dynamic Random Subgraph Model

Proceedings of the 23-th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2015)International audienceIn recent years, many random graph models have been proposed to extract information from networks. The principle is to look for groups of vertices with homogenous connection profiles. Most of these models are suitable for static networks and can handle different types of edges. This work is motivated by the need of analyzing an evolving network describing email communications between employees of the Enron compagny where social positions play an important role. Therefore, in this paper, we consider the random subgraph model (RSM) which was proposed recently to model networks through latent clusters built within known partitions. Using a state space model to characterize the cluster proportions, RSM is then extended in order to deal with dynamic networks. We call the latter the dynamic random subgraph model (dRSM)

Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey

Dynamic networks are used in a wide range of fields, including social network analysis, recommender systems, and epidemiology. Representing complex networks as structures changing over time allow network models to leverage not only structural but also temporal patterns. However, as dynamic network literature stems from diverse fields and makes use of inconsistent terminology, it is challenging to navigate. Meanwhile, graph neural networks (GNNs) have gained a lot of attention in recent years for their ability to perform well on a range of network science tasks, such as link prediction and node classification. Despite the popularity of graph neural networks and the proven benefits of dynamic network models, there has been little focus on graph neural networks for dynamic networks. To address the challenges resulting from the fact that this research crosses diverse fields as well as to survey dynamic graph neural networks, this work is split into two main parts. First, to address the ambiguity of the dynamic network terminology we establish a foundation of dynamic networks with consistent, detailed terminology and notation. Second, we present a comprehensive survey of dynamic graph neural network models using the proposed terminologyComment: 28 pages, 9 figures, 8 table

Nonparametric Bayes dynamic modeling of relational data

Symmetric binary matrices representing relations among entities are commonly collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being in inference on the relationship structure and prediction. We propose a nonparametric Bayesian dynamic model, which reduces dimensionality in characterizing the binary matrix through a lower-dimensional latent space representation, with the latent coordinates evolving in continuous time via Gaussian processes. By using a logistic mapping function from the probability matrix space to the latent relational space, we obtain a flexible and computational tractable formulation. Employing P\`olya-Gamma data augmentation, an efficient Gibbs sampler is developed for posterior computation, with the dimension of the latent space automatically inferred. We provide some theoretical results on flexibility of the model, and illustrate performance via simulation experiments. We also consider an application to co-movements in world financial markets

A dynamic network model with persistent links and node-specific latent variables, with an application to the interbank market

We propose a dynamic network model where two mechanisms control the probability of a link between two nodes: (i) the existence or absence of this link in the past, and (ii) node-specific latent variables (dynamic fitnesses) describing the propensity of each node to create links. Assuming a Markov dynamics for both mechanisms, we propose an Expectation-Maximization algorithm for model estimation and inference of the latent variables. The estimated parameters and fitnesses can be used to forecast the presence of a link in the future. We apply our methodology to the e-MID interbank network for which the two linkage mechanisms are associated with two different trading behaviors in the process of network formation, namely preferential trading and trading driven by node-specific characteristics. The empirical results allow to recognise preferential lending in the interbank market and indicate how a method that does not account for time-varying network topologies tends to overestimate preferential linkage.Comment: 19 pages, 6 figure