Abstract

Identifying change points and/or anomalies in dynamic network structures has become increasingly popular across various domains, from neuroscience to telecommunication to finance. One particular objective of anomaly detection from a neuroscience perspective is the reconstruction of the dynamic manner of brain region interactions. However, most statistical methods for detecting anomalies have the following unrealistic limitation for brain studies and beyond: that is, network snapshots at different time points are assumed to be independent. To circumvent this limitation, we propose a distribution-free framework for anomaly detection in dynamic networks. First, we present each network snapshot of the data as a linear object and find its respective univariate characterization via local and global network topological summaries. Second, we adopt a change point detection method for (weakly) dependent time series based on efficient scores, and enhance the finite sample properties of change point method by approximating the asymptotic distribution of the test statistic using the sieve bootstrap. We apply our method to simulated and to real data, particularly, two functional magnetic resonance imaging (fMRI) datasets and the Enron communication graph. We find that our new method delivers impressively accurate and realistic results in terms of identifying locations of true change points compared to the results reported by competing approaches. The new method promises to offer a deeper insight into the large-scale characterizations and functional dynamics of the brain and, more generally, into the intrinsic structure of complex dynamic networks. Supplemental materials for this article are available online.

摘要

识别动态网络结构中的变化点和/或异常在各个领域变得越来越流行，从神经科学到电信再到金融。从神经科学的角度来看，异常检测的一个特定目标是重建大脑区域相互作用的动态方式。然而，大多数用于检测异常的统计方法对大脑研究及其他研究具有以下不切实际的限制：即，假设不同时间点的网络快照是独立的。为了规避这一限制，我们提出了一个用于动态网络异常检测的无分布框架。首先，我们将数据的每个网络快照呈现为一个线性对象，并通过局部和全局网络拓扑摘要找到其各自的单变量特征。第二，我们采用基于有效分数的（弱）相关时间序列的变化点检测方法，并通过使用筛网引导程序逼近检验统计量的渐近分布来增强变化点方法的有限样本特性。我们将我们的方法应用于模拟数据和真实数据，特别是两个功能磁共振成像 (fMRI) 数据集和安然通信图。我们发现，与竞争方法报告的结果相比，我们的新方法在识别真实变化点的位置方面提供了令人印象深刻的准确和逼真的结果。这种新方法有望更深入地了解大脑的大规模表征和功能动力学，更一般地说，可以深入了解复杂动态网络的内在结构。