# Optimal Change Point Detection and Localization in Sparse Dynamic Networks

arXiv: https://arxiv.org/abs/1809.09602 · HTML: https://mlsanity.com/paper/1809.09602/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2018.

## Built on by (most cited first, 9 of 9)

- [Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition](https://mlsanity.com/paper/2106.16042/) (2021)
- [Optimal network online change point localisation](https://mlsanity.com/paper/2101.05477/) (2021)
- [Segmenting Human-LLM Co-authored Text via Change Point Detection](https://mlsanity.com/paper/2605.03723/) (2026)
- [Graph similarity learning for change-point detection in dynamic networks](https://mlsanity.com/paper/2203.15470/) (2022)
- [Segmentation of high dimensional means over multi-dimensional change points and connections to regression trees](https://mlsanity.com/paper/2105.10017/) (2021)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [Latent Evolution Model for Change Point Detection in Time-varying Networks](https://mlsanity.com/paper/2212.08818/) (2022)
- [Semisupervised regression in latent structure networks on unknown manifolds](https://mlsanity.com/paper/2305.02473/) (2023)
- [Inferring Change Points in High-Dimensional Regression via Approximate Message Passing](https://mlsanity.com/paper/2404.07864/) (2024)

## Abstract (arXiv)

We study the problem of change point localization in dynamic networks models. We assume that we observe a sequence of independent adjacency matrices of the same size, each corresponding to a realization of an unknown inhomogeneous Bernoulli model. The underlying distribution of the adjacency matrices are piecewise constant, and may change over a subset of the time points, called change points. We are concerned with recovering the unknown number and positions of the change points. In our model setting we allow for all the model parameters to change with the total number of time points, including the network size, the minimal spacing between consecutive change points, the magnitude of the smallest change and the degree of sparsity of the networks. We first identify a region of impossibility in the space of the model parameters such that no change point estimator is provably consistent if the data are generated according to parameters falling in that region. We propose a computationally-simple algorithm for network change point localization, called Network Binary Segmentation, that relies on weighted averages of the adjacency matrices. We show that Network Binary Segmentation is consistent over a range of the model parameters that nearly cover the complement of the impossibility region, thus demonstrating the existence of a phase transition for the problem at hand. Next, we devise a more sophisticated algorithm based on singular value thresholding, called Local Refinement, that delivers more accurate estimates of the change point locations. Under appropriate conditions, Local Refinement guarantees a minimax optimal rate for network change point localization while remaining computationally feasible.