We estimate the time-varying Gaussian graphical models under smoothness assumptions on both covariance matrix and graph structure.
Most methods for Gaussian graphical models assume i.i.d. observations. However, the conditional independence relationships may evolve when data are measured over time. Zhou et al. (2010) and Wang and Kolar (2014) assume the covariance matrix changes smoothly. However, the former ignores potential graph structural smoothness and the latter assumes a time-invariant graph which is often too restrictive.
We propose a method that utilizes both parameter smoothness and structural smoothness through a local group-lasso type penalty. It is able to more efficiently borrow information across time and allows the estimated graphs to (smoothly) change over time. We discuss an ADMM algorithm for model fitting and use cross validation for tuning. We show that the proposed method is able to improve on both model selection and parameter estimation by simulation studies.
A more efficient algorithm based on pseudo-likelihood approximations (Peng et al. (2009)) is also proposed. We show that it reduce the time complexity while maintain the method performance.
|