Forward-Backward Splitting for Time-Varying Graphical Models

Gaussian graphical models have received much attention in the last years, due to their flexibility and expression power. However, the optimisation of such complex models suffer from computational issues both in terms of convergence rates and memory requirements. Here, we present a forward-backward splitting (FBS) procedure for Gaussian graphical modelling of multivariate time-series which relies on recent theoretical studies ensuring convergence under mild assumptions. Our experiments show that a FBS-based implementation achieves, with very fast convergence rates, optimal results with respect to ground truth and standard methods for dynamical network inference. Optimisation algorithms which are usually exploited for network inference suffer from drawbacks when considering large sets of unknowns. Particularly for increasing data sets and model complexity, we argue for the use of fast and theoretically sound optimisation algorithms to be significant to the graphical modelling community.