# Change point localization in dependent dynamic nonparametric random dot product graphs

arXiv: https://arxiv.org/abs/1911.07494 · HTML: https://mlsanity.com/paper/1911.07494/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2019.

## Built on by (most cited first, 5 of 5)

- [Online Change Point Detection for Weighted and Directed Random Dot Product Graphs](https://mlsanity.com/paper/2201.11222/) (2022)
- [Graph similarity learning for change-point detection in dynamic networks](https://mlsanity.com/paper/2203.15470/) (2022)
- [Network two-sample test for block models](https://mlsanity.com/paper/2406.06014/) (2024)
- [Concentration inequalities for correlated network-valued processes with applications to community estimation and changepoint analysis](https://mlsanity.com/paper/2208.01365/) (2022)
- [Implications of sparsity and high triangle density for graph representation learning](https://mlsanity.com/paper/2210.15277/) (2022)

## Abstract (arXiv)

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.