Scalable Estimation for Popularity-adjusted Latent Space Models for Network Data

In network modelling, edges are inherently interdependent: for instance, if you express interest in this project and contact me, it is more likely that a friend of yours, specifically one who shares similar interests and studies mathematics, will do the same. This interdependence complicates the statistical modelling of relational data, such as email communication networks. A widely used approach to address this complexity is the Latent Space Model (LSM), which assumes that each actor occupies a position in an unobserved latent space, and that the probability of a tie between any two actors is a function of the distance between their latent positions. To account for unobserved heterogeneity in node activity (e.g., popularity or sociability), these models are often augmented with actor-specific fixed effects. However, such modifications substantially increase the dimensionality of the parameter space, making inference and estimation more computationally intensive, particularly as network size increases. This challenge is increasingly relevant as empirical networks grow in scale and complexity. This Final Year Project will build on recent advances in Stochastic Gradient Descent (SGD) and Majorization-Minimisation (MM) optimisation techniques to develop scalable algorithms for estimating popularity-adjusted Latent Space Models. Interest in network modelling and numerical optimisation is a prerequisite. All interested students must first email fritzc@tcd.ie to set up a short informal meeting to discuss the project.