Gaussian Belief Propogation: From Theory to Applications

In this lecture, we present a tutorial overview of a powerful class of probabilistic graphical models called factor graphs and specialize their model in the large-scale multivariate Gaussian distribution setting. Our focus is on Gaussian Belief Propagation (GBP), a simple, efficient and widely applicable algorithm for probabilistic inference on factor graphs. We discuss the key issues of GBP applied in real-world probabilistic systems, such as correctness, convergence and complexity through the prism of GBP applications in the fundamental problem of state estimation in power systems. Future extensions of these concepts using the modern data-based machine (deep) learning tools are also presented as our ongoing work.