Abstract
Network data frequently represents interactions between actors. The latent position model is a widely used approach for dimensionality reduction, analysis, and visualization of such data. The model positions actors in a lower-dimensional latent space and assumes that the probability of a link between any pair of actors is a function of their distance in this space. However, inferring the dimension of this space remains a challenge. Previous approaches either simplify the problem by using two dimensions or rely on model selection criteria that incur in the computational expense of fitting multiple models. To address this issue, we present the latent shrinkage position model, which automatically infers the effective dimension of the latent space. The approach employs a novel Bayesian nonparametric multiplicative truncated gamma process prior that ensures shrinkage of the variance of the latent positions as the number of dimensions increases. As a result, dimensions with non-negligible variance are deemed the most useful to describe the observed network, inducing automatic inference of the latent space dimension. Inference proceeds via a Markov chain Monte Carlo algorithm, where tailored surrogate proposal distributions reduce the computational burden. We assess the model's properties through simulation studies and illustrate its utility through application to real network datasets.
Organizzazione
Laura Anderlucci