Compressive Nonparametric Graphical Model Selection For Time Series
This addresses the challenge of graphical model selection in high-dimensional time series for statisticians and data scientists, offering a nonparametric and compressive method.
The paper tackles the problem of inferring conditional independence graphs for high-dimensional Gaussian time series from limited samples without parametric assumptions, achieving correct graph identification with high probability under analytical conditions.
We propose a method for inferring the conditional indepen- dence graph (CIG) of a high-dimensional discrete-time Gaus- sian 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 proper- ties. 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.