A Nonparametric Approach for Learning Noncausal Dynamic Graphs

The paper considers the problem to learn symmetric networks whose edges encode noncausal dynamic relations among the node variables. We propose a new covariance extension problem and we show that the solution maximizing the entropy, whose definition is based on the notion of transportation distance, exists and is unique. Moreover, the solution corresponds to a noncausal dynamic graph whose topology is determined by the selected entries in the moment constraints. We propose a regularized version of such estimator in the case that the graph topology is unknown. Then, we generalize the paradigm to a nonparametric model class, including the case where the network is in a feedback configuration. Finally, we test the performance of the proposed method through some numerical experiments.