Learning the Conditional Independence Structure of Stationary Time Series: A Multitask Learning Approach
This addresses the challenge of graph inference in time series analysis for researchers in statistics and machine learning, offering a non-parametric alternative that is robust to model assumptions.
The paper tackles the problem of inferring conditional independence graphs for high-dimensional Gaussian time series without relying on parametric models, achieving consistent results with small sample sizes when the graph is sparse, as validated by numerical experiments showing superior performance under model mismatch.
We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector 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. The proposed inference scheme works even for sample sizes much smaller than the number of scalar process components if the true underlying CIG is sufficiently sparse. A theoretical performance analysis provides conditions which guarantee that the probability of the proposed inference method to deliver a wrong CIG is below a prescribed value. These conditions imply lower bounds on the sample size such that the new method is consistent asymptotically. Some numerical experiments validate our theoretical performance analysis and demonstrate superior performance of our scheme compared to an existing (parametric) approach in case of model mismatch.