Graphical Inference in Linear-Gaussian State-Space Models

State-space models (SSM) are central to describe time-varying complex systems in countless signal processing applications such as remote sensing, networks, biomedicine, and finance name a few. Inference prediction SSMs possible when the model parameters known, which is rarely case. The estimation of these crucial, not only for performing statistical analysis, but also uncovering underlying structure phenomena. In this paper, we focus on linear-Gaussian model, arguably most celebrated SSM, particularly challenging task estimating transition matrix that encodes Markovian dependencies evolution multi-variate state. We introduce novel perspective by relating adjacency directed graph, interpreted causal relationship among state dimensions Granger-causality sense. Under perspective, propose new method called GraphEM based well sounded expectation-maximization (EM) methodology inferring jointly with smoothing/filtering observed data. an advanced convex optimization solver relying consensus-based implementation proximal splitting strategy solving M-step. This approach enables efficient versatile various sophisticated priors graph structure, parsimony constraints, while benefiting from convergence guarantees. demonstrate good performance interpretable results means two sets numerical examples.