Change point localization in dependent dynamic nonparametric random dot product graphs
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In this paper, we study the change point localization problem in a sequence of dependent nonparametric random dot product graphs (e.g. Young and Scheinerman, 2007). To be specific, assume that at every time point, a network is generated from a nonparametric random dot product graph model, 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 the edge-dependence within networks and across-time dependence between networks, which is the most flexible setting in the published literature. To fulfill 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, the theoretical result thereof is a refined version of the state-of-the-art results, allowing the dimension of the latent positions to grow unbounded. Then, we construct a nonparametric version of CUSUM statistic (e.g. Page,1954; Padilla et al. 2019) that can handle across-time dependence. The consistency is proved theoretically and supported by extensive numerical experiments, which outperform existing methods.
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