Sequential change-point detection in high-dimensional Gaussian graphical models
Sequential change-point detection in high-dimensional Gaussian graphical models
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发表时间：
2018-06
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通讯作者：
Hossein Keshavarz;G. Michailidis;Y. Atchadé
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作者：
Hossein Keshavarz;G. Michailidis;Y. Atchadé
高维分段平稳图形模型代表了一个多用途的类，用于建模时变网络出现在不同的应用领域，包括生物学，经济学和社会科学。最近在稀疏图形模型拓扑中状态变化的离线检测和估计方面已经有了一些工作。然而，尽管在线设置与传感器网络和其他工程监测系统以及金融市场的应用高度相关，但在线设置在很大程度上仍未被探索。为此，本工作引入了一种新的可扩展在线算法，用于检测具有小延迟的稀疏高斯图形模型的逆协方差矩阵中未知数量的突变。该算法基于对网络中所有节点的条件对数似然的监测，可以扩展到大量的连续和离散图形模型。我们还研究了我们的过程在图大小、稀疏度水平、样本数量以及网络拓扑的前后变化等温和规则条件下的渐近性质。对合成数据和实际数据的数值研究表明，所提出的方法在计算和统计效率方面具有良好的性能。
High dimensional piecewise stationary graphical models represent a versatile class for modelling time varying networks arising in diverse application areas, including biology, economics, and social sciences. There has been recent work in offline detection and estimation of regime changes in the topology of sparse graphical models. However, the online setting remains largely unexplored, despite its high relevance to applications in sensor networks and other engineering monitoring systems, as well as financial markets. To that end, this work introduces a novel scalable online algorithm for detecting an unknown number of abrupt changes in the inverse covariance matrix of sparse Gaussian graphical models with small delay. The proposed algorithm is based upon monitoring the conditional log-likelihood of all nodes in the network and can be extended to a large class of continuous and discrete graphical models. We also investigate asymptotic properties of our procedure under certain mild regularity conditions on the graph size, sparsity level, number of samples, and pre- and post-changes in the topology of the network. Numerical works on both synthetic and real data illustrate the good performance of the proposed methodology both in terms of computational and statistical efficiency across numerous experimental settings.