Inference of Time–Varying Graph Topologies via Gaussian Processes

In this paper, we explore the estimation of directed time-varying graph topologies, which represent evolving relationships among nodes in high-dimensional, interdependent data. We introduce a novel fully Bayesian method based on Gaussian processes, employing random walks to model the time-varying edge weights with time. This approach accommodates nonlinear and time-varying lagged relationships among time series. We implement the proposed method using the Hamiltonian Monte Carlo method. Numerical tests reveal that our method performs very well and is comparable to state-of-the-art methods, making it a promising tool for unveiling dynamic graph structures and causality.