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February 2021 Optimal change point detection and localization in sparse dynamic networks
Daren Wang, Yi Yu, Alessandro Rinaldo
Ann. Statist. 49(1): 203-232 (February 2021). DOI: 10.1214/20-AOS1953

Abstract

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.

Citation

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Daren Wang. Yi Yu. Alessandro Rinaldo. "Optimal change point detection and localization in sparse dynamic networks." Ann. Statist. 49 (1) 203 - 232, February 2021. https://doi.org/10.1214/20-AOS1953

Information

Received: 1 September 2018; Revised: 1 November 2019; Published: February 2021
First available in Project Euclid: 29 January 2021

Digital Object Identifier: 10.1214/20-AOS1953

Subjects:
Primary: 62M10
Secondary: 91B84

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 1 • February 2021
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