  The time-evolving precision matrix of a piecewise-constant Gaussian graphical
model encodes the dynamic conditional dependency structure of a multivariate
time-series. Traditionally, graphical models are estimated under the assumption
that data is drawn identically from a generating distribution. Introducing
sparsity and sparse-difference inducing priors we relax these assumptions and
propose a novel regularized M-estimator to jointly estimate both the graph and
changepoint structure. The resulting estimator possesses the ability to
therefore favor sparse dependency structures and/or smoothly evolving graph
structures, as required. Moreover, our approach extends current methods to
allow estimation of changepoints that are grouped across multiple dependencies
in a system. An efficient algorithm for estimating structure is proposed. We
study the empirical recovery properties in a synthetic setting. The qualitative
effect of grouped changepoint estimation is then demonstrated by applying the
method on two real-world data-sets.
