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.

本文提出了一种基于稀疏差异先验的正则化 M - 估计方法，通过估计图和变化点结构相结合，探讨了多变量时序的时间变化精度矩阵的动态条件依赖结构，以及其应对于稀疏依赖结构或平滑演化图结构的需求。此外，方法的扩张能使得在多个系统的依赖关系中进行变化点的估计，并提出了一种高效算法用于对结构的估计，最后，对两个真实世界数据集的定性影响以及合理性进行研究。