Nonparametric Compressive Graphical Model Selection for Vector-Valued Stationary Random Processes: A Multitask Learning Approach

We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian time series (discrete time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a parametric process model (such as, e.g., an autoregressive model) for the observed random process. Instead, we only require certain smoothness properties (in the Fourier domain) of the process only. The proposed inference scheme is compressive in that it works even for sample sizes much smaller than the number of scalar process components. A theoretical performance analysis provides conditions which guarantee that the probability of the proposed inference method to deliver a wrong the CIG is below a prescribed value. This analysis reveals conditions for the new method to be consistent asymptotically. Some numerical experiments validate our theoretical performance analysis and demonstrate superior performance of our scheme compared to existing approaches in case of model mismatch.