Network inference and change point detection for piecewise-stationary time series

Graphical models are powerful tools to describe complex systems. Especially sparse graphical models are currently en vogue, as they allow us to infer network structure from multiple time series (e.g., functional brain networks from multichannel electroencephalograms). So far, most of the literature deals with stationary time series, whereas real-life time series often exhibit non-stationarity. In this paper, techniques are proposed to infer graphical models from piecewise stationary time series; first change point are detected in the time series, and then graphical models are inferred for each stationary segment. Specifically, a low-complexity algorithm based on Pruned Exact Linear Time method is proposed to identify change points. Copula Gaussian graphical models (with and without hidden variables) are then generated for each stationary segment. The crux of the proposed approach is that it determines the number and location of the change points as well as the graphical models in a fully automated manner. Results for both synthetic data and scalp electroencephalograms of epileptic seizure patients are provided to validate the model.