Change point localization in dependent dynamic nonparametric random dot product graphs
Change point localization in dependent dynamic nonparametric random dot product graphs
复制标题
DOI：
--
复制
发表时间：
2019-11
期刊：
影响因子：
--
通讯作者：
Oscar Hernan Madrid Padilla;Yi Yu;C. Priebe
中科院分区：
文献类型：
--
作者：
Oscar Hernan Madrid Padilla;Yi Yu;C. Priebe
本文研究了相依非参数随机点积图序列的变点定位问题。具体而言，假设在每个时间点，从非参数随机点积图模型生成网络（参见例如Athreya等人，2017），其中潜在位置是从未知的底层分布生成的。潜在的分布在时间上是分段恒定的，并且在未知的位置发生变化，称为变化点。最重要的是，我们允许两个连续变化点之间生成的网络之间的依赖性。这种设置结合了网络内的边缘依赖性和网络间的时间依赖性，这是已发表文献中最灵活的设置。为了完成一致定位变化点的任务，我们提出了一种新的变化点检测算法，包括两个步骤。首先，我们估计的随机点积模型的潜在位置，我们的理论结果是一个完善的版本的国家的最先进的结果，允许的潜在位置的尺寸无限增长。随后，我们构建了一个非参数版本的PADUM统计量（Page，1954，帕迪利亚等人，2019年），允许时间依赖性。一致的本地化的理论证明和支持广泛的数值实验，说明了国家的最先进的性能。我们还提供了可能的扩展的深入讨论，以提供更多的理解和见解。
In this paper, we study the change point localization problem in a sequence of dependent nonparametric random dot product graphs. To be specific, assume that at every time point, a network is generated from a nonparametric random dot product graph model (see e.g. Athreya et al., 2017), where the latent positions are generated from unknown underlying distributions. The underlying distributions are piecewise constant in time and change at unknown locations, called change points. Most importantly, we allow for dependence among networks generated between two consecutive change points. This setting incorporates edge-dependence within networks and temporal dependence between networks, which is the most flexible setting in the published literature. To accomplish the task of consistently localizing change points, we propose a novel change point detection algorithm, consisting of two steps. First, we estimate the latent positions of the random dot product model, our theoretical result being a refined version of the state-of-the-art results, allowing the dimension of the latent positions to grow unbounded. Subsequently, we construct a nonparametric version of the CUSUM statistic (Page, 1954, Padilla et al., 2019) that allows for temporal dependence. Consistent localization is proved theoretically and supported by extensive numerical experiments, which illustrate state-of-the-art performance. We also provide in depth discussion of possible extensions to give more understanding and insights.