Spatially Informed Network Identification

Understanding high-dimensional data often requires learning network models, which are particularly useful when the network is sparse or has a specific structure. In this paper, we focus on network models whose edges encode Granger causality relations and whose topology depends on spatial information. Specifically, we introduce an identification paradigm based on the kernel-based Prediction Error Method (PEM), which incorporates spatial dependencies into the model selection process. Our main contribution is the design of a kernel matrix that embeds spatial information using the maximum entropy principle. The effectiveness of the proposed approach is demonstrated through a numerical experiment.