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February 2018 Change point detection in network models: Preferential attachment and long range dependence
Shankar Bhamidi, Jimmy Jin, Andrew Nobel
Ann. Appl. Probab. 28(1): 35-78 (February 2018). DOI: 10.1214/17-AAP1297

Abstract

Inspired by empirical data on real world complex networks, the last few years have seen an explosion in proposed generative models to understand and explain observed properties of real world networks, including power law degree distribution and “small world” distance scaling. In this context, a natural question is how to understand the effect of change points—how abrupt changes in parameters driving the network model change structural properties of the network. We study this phenomenon in one popular class of dynamically evolving networks: preferential attachment models. We derive asymptotic properties of various functionals of the network including the degree distribution as well as maximal degree asymptotics, in essence showing that the change point does effect the degree distribution but does not change the degree exponent. This provides evidence for long range dependence and sensitive dependence of the evolution of the network on the initial evolution of the process. We propose an estimator for the change point and prove consistency properties of this estimator. The methodology developed highlights the effect of the nonergodic nature of the evolution of the network on classical change point estimators.

Citation

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Shankar Bhamidi. Jimmy Jin. Andrew Nobel. "Change point detection in network models: Preferential attachment and long range dependence." Ann. Appl. Probab. 28 (1) 35 - 78, February 2018. https://doi.org/10.1214/17-AAP1297

Information

Received: 1 June 2016; Revised: 1 December 2016; Published: February 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06873679
MathSciNet: MR3770872
Digital Object Identifier: 10.1214/17-AAP1297

Subjects:
Primary: 05C80, 60C05

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.28 • No. 1 • February 2018
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