  In this paper, we study the offline 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 \citep[see e.g.][]{athreya2017statistical},
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 diverge. Subsequently, we construct a
nonparametric version of the CUSUM statistic \citep[e.g.][]{Page1954,
padilla2019optimal} 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.
