Modeling Network Populations via Graph Distances

This article introduces a new class of models for multiple networks. The core idea is to parametrize a distribution on labelled graphs in terms of a Fréchet mean graph (which depends on a user-specified choice of metric or graph distance) and a parameter that controls the concentration of this distribution about its mean. Entropy is the natural parameter for such control, varying from a point mass concentrated on the Fréchet mean itself to a uniform distribution over all graphs on a given vertex set. We provide a hierarchical Bayesian approach for exploiting this construction, along with straightforward strategies for sampling from the resultant posterior distribution. We conclude by demonstrating the efficacy of our approach via simulation studies and two multiple-network data analysis examples: one drawn from systems biology and the other from neuroscience

Geometric Representations of Random Hypergraphs

We introduce a novel parameterization of distributions on hypergraphs based on the geometry of points in Rd. The idea is to induce distributions on hypergraphs by placing priors on point configurations via spatial processes. This specification is then used to infer conditional independence models, or Markov structure, for multivariate distributions. This approach results in a broader class of conditional independence models beyond standard graphical models. Factorizations that cannot be retrieved via a graph are possible. Infer- ence of nondecomposable graphical models is possible without requiring decomposability, or the need of Gaussian assumptions. This approach leads to new Metropolis-Hastings Markov chain Monte Carlo algorithms with both local and global moves in graph space, generally offers greater control on the distribution of graph features than currently possible, and naturally extends to hypergraphs. We provide a comparative performance evaluation against state-of-the-art approaches, and illustrate the utility of this approach on simulated and real data

Latent Space Representations of Hypergraphs

The increasing prevalence of relational data describing interactions among a target population has motivated a wide literature on statistical network analysis. In many applications, interactions may involve more than two members of the population and this data is more appropriately represented by a hypergraph. In this paper we present a model for hypergraph data which extends the latent space distance model of Hoff et al. (2002) and, by drawing a connection to constructs from computational topology, we develop a model whose likelihood is inexpensive to compute. We obtain posterior samples via an MCMC scheme and we rely on Bookstein coordinates to remove the identifiability issues associated with the latent representation. We demonstrate that the latent space construction imposes desirable properties on the hypergraphs generated in our framework and provides a convenient visualisation of the data. Furthermore, through simulation, we investigate the flexibility of our model and consider estimating predictive distributions. Finally, we explore the application of our model to a real world co-occurrence dataset

Telling the Researcher STOR-i With Data Science:Elsevier data scientists are working with Lancaster University researchers to advance our understanding of researcher behaviors

At Elsevier, we aim to help researchers make new discoveries, collaborate with their colleagues, and give them the knowledge they need to find funding. That means developing a deep understanding of researchers’ work so we can create tools that help them find what they need when they need it. Our recent collaboration with Lancaster University shows how network analysis can help us understand how researchers work and what they need