B0517
Title: Spike-and-slab priors for dimension selection in static and dynamic network eigenmodels
Authors: Joshua Loyal - Florida State University (United States) [presenting]
Yuguo Chen - University of Illinois at Urbana-Champaign (United States)
Abstract: Latent space models (LSMs) are frequently used to model network data by embedding a network's nodes into a low-dimensional latent space; however, correctly choosing the dimension of this space remains a challenge. The contribution is two-fold. First, we propose a new Bayesian LSM for dynamic networks that not only fixes parameter identifiability issues that have previously impeded dimension selection but also models a larger class of dynamic networks than previous approaches. Second, we propose a Bayesian approach to dimension selection for static and dynamic LSMs based on an ordered spike-and-slab prior that provides improved dimension estimation and satisfies several appealing theoretical properties. In particular, we show that the static model's posterior concentrates on low-dimensional models near the truth. These models are accompanied by a novel parameter expansion scheme that allows for efficient MCMC estimation using a Metropolis-within-Gibbs sampler with Hamiltonian Monte Carlo proposals. We demonstrate our approach's versatility and consistent dimension selection on simulated networks. Lastly, we use the static and dynamic models to study a static protein interaction network and the global arms trades dynamics during the Cold War.
