On 10 February 2016 the Royal Statistical Society's Applied Probability section held a meeting on Networks at Errol Street. There were four speakers covering a range of topics on networks.
Mark Newman (University of Michigan) spoke on large-scale structure in networks and the limits of detectability. Mark gave an overview on different forms of network structure, and then focussed on community structure in networks. He reviewed spectral methods for inference in stochastic block models and why these methods fail for very sparse networks. Then he presented a Bayesian approach and inference using message passing. He clearly explained the detectability threshold for community structure in stochastic block models. The talk concluded with further ideas on detecting overlapping groups, core-periphery structure, network hierarchies and latent-space structure. The talk was illustrated with many examples such as a dating network, a neural network, and a school friendship network.
Sofia Olhede (University College, University of London) spoke on nonparametric network summaries. She focussed on local patterns in networks, which she captured through rooted motif counts. She provided asymptotic results for the counts and for functions of the counts, including normal approximations, and related them to kernel-based models as well as to stochastic block models. The results were illustrated using political blog data as well as citation networks.
Marc Lelarge (INRIA, Paris) spoke on community detection with the non-backtracking operator. His talk went deeply into the derivation of the detectability threshold for community structure in stochastic block models. His proof used connections between random matrix theory and network analysis through spectral analysis based on the non-backtracking operator. He also gave new results on the largest eigenvalues of the non-backtracking operator in the case of Bernoulli random graphs and in the case of stochastic block models with two groups.
Johan Koskinen (University of Manchester) spoke on Bayesian data-augmentation for estimation of exponential random graph models for partially observed multi-layered networks. He gave a thorough introduction to exponential random graph models, with special emphasis on estimation problems. He illustrated how a social circuit assumption can overcome these issues. Johan then considered partially observed data, and used an exchange algorithm to carry out inference for such data. He illustrated the results with a terrorist network of Noordin Mohamed Top and with a social network of suffragettes.