Many modern day datasets exhibit multivariate dependance structure that can be modelled using networks or graphs. For example, in social sciences, biomedical studies, financial applications etc. the association of datasets with latent network structures are ubiquitous. Many of these datasets are time-varying in nature and that motivates the modelling of dynamic networks. In this talk I will present some of our recent research which looks at the challenging task of recovering such networks, even in high-dimensional settings.
Our approach studies the canonical Gaussian graphical model whereby patterns of variable dependence are encoded through partial correlation structure. I will demonstrate how regularisation ideas such as the graphical lasso may be implemented when data is drawn i.i.d. but how this may fail in non-stationary settings. I will then present an overview of our work (with Sandipan Roy, UCL) which extends such methods to dynamic settings. By furnishing appropriate convex M-estimators that enforce smoothness and sparsity assumptions on the Gaussian we demonstrate an ability to recover the true underlying network structure. I will present both synthetic experiments and theoretical analysis which shed light on the performance of these methods.