We consider the consistency properties of a regularised estimator for the simultaneous identification of both changepoints and graphical dependency structure in multivariate time-series. Traditionally, estimation of Gaussian graphical models (GGM) is performed in an i.i.d setting. More recently, such models have been extended to allow for changes in the distribution, but primarily where changepoints are known a priori. In this work, we study the Group-Fused Graphical Lasso (GFGL) which penalises partial correlations with an L1 penalty while simultaneously inducing block-wise smoothness over time to detect multiple changepoints. We present a proof of consistency for the estimator, both in terms of changepoints, and the structure of the graphical models in each segment. We contrast our results, which are based on a global, i.e. graph-wide likelihood, with those previously obtained for performing dynamic graph estimation at a node-wise (or neighbourhood) level.

中文翻译：

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具有融合高斯图形模型的一致多变点估计

我们考虑了正则化估计器的一致性属性，用于同时识别多元时间序列中的变化点和图形依赖结构。传统上，高斯图形模型 (GGM) 的估计是在 iid 设置中执行的。最近，此类模型已被扩展以允许分布发生变化，但主要是在先验已知变化点的情况下。在这项工作中，我们研究了 Group-Fused Graphical Lasso (GFGL)，它用 L1 惩罚惩罚部分相关性，同时随着时间的推移诱导块级平滑以检测多个变化点。我们在变化点和每个段中图形模型的结构方面为估计器提供了一致性证明。我们对比了我们的结果，这些结果基于全局，即图范围的可能性，