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 random process from finite-length observations. Our approach does not rely on a parametric model (such as, e.g., an autoregressive model) for the vector random process; rather, it only assumes certain spectral smoothness properties. 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 for our method to correctly identify the CIG with high probability.