We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when at most one change point occurs and generalize them to multiple change points settings. The proposed statistics leverage edge weight information in the graphs, exhibiting substantial improvements in testing power and localization accuracy in simulations. We derive the null limiting distribution, provide accurate analytic approximations to control type I error, and establish theoretical guarantees on the power consistency under contiguous alternatives for the one change point setting, as well as the minimax localization rate. In the multiple change points setting, the asymptotic correctness of the number and location of change points are also guaranteed. The methods are illustrated on the MIT proximity network data.

翻译：我们考虑在离线观测序列分布中检测和定位变化点。根据使用类似观测图的非参数框架,我们提议在最多出现一个变化点时进行新的测试统计,并将其推广到多个变化点设置。拟议统计数据在图形中利用边缘权重信息,在模拟中测试功率和本地化准确度方面显示出显著改进。我们得出了无效限制分布,提供了准确的分析近似值以控制类型I的错误,并为一个变化点设置的相连替代物下的权力一致性以及最小本地化率建立了理论保障。在多个变化点设置中,还保证了变化点数量和位置的无保护性正确性。这些方法在麻省理工学院近距离网络数据中作了说明。