Compressive Nonparametric Graphical Model Selection For Time Series

We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional discrete-time Gaussian vector-process from finite-length observations. Our approach does not rely on a parametric process model (such as, e.g., an autoregressive model) for the vector random process, but needs certain smoothness properties of the process only. The proposed inference scheme is compressive in that it works for sample sizes that are much smaller than the number of scalar process components. We provide analytical conditions guaranteeing that the probability of the proposed inference method correctly identifying the CIG is above a prescribed value. Our analysis also reveals conditions for the new method to be consistent asymptotically.