Variational bayes learning of time-varying graphical models

We propose a tuning-free Bayesian approach to learn a set of sparse graphical models, in which adjacent graphs share similar structures. This model can be applied to estimating dynamic networks that evolve smoothly with regard to a covariate (e.g., time). Specifically, a novel structured spike and slab prior is constructed. This prior allows time-varying sparsity pattern by smoothing the spike probabilities across time using a Gauss-Markov chain. An efficient variational Bayes (VB) algorithm is then derived to learn the model, and is compared to related frequentist methods in the literature. We further extend the proposed mechanism to learn graphical models for multivariate time series in frequency domain. As an example, we analyze scalp electroencephalograms (EEG) recordings of patients at early stages of Alzheimer disease (AD), and quantify the loss of synchrony in comparison with control subjects.