Open Access
2020 Vertex nomination, consistent estimation, and adversarial modification
Joshua Agterberg, Youngser Park, Jonathan Larson, Christopher White, Carey E. Priebe, Vince Lyzinski
Electron. J. Statist. 14(2): 3230-3267 (2020). DOI: 10.1214/20-EJS1744


Given a pair of graphs $G_{1}$ and $G_{2}$ and a vertex set of interest in $G_{1}$, the vertex nomination (VN) problem seeks to find the corresponding vertices of interest in $G_{2}$ (if they exist) and produce a rank list of the vertices in $G_{2}$, with the corresponding vertices of interest in $G_{2}$ concentrating, ideally, at the top of the rank list. In this paper, we define and derive the analogue of Bayes optimality for VN with multiple vertices of interest, and we define the notion of maximal consistency classes in vertex nomination. This theory forms the foundation for a novel VN adversarial contamination model, and we demonstrate with real and simulated data that there are VN schemes that perform effectively in the uncontaminated setting, and adversarial network contamination adversely impacts the performance of our VN scheme. We further define a network regularization method for mitigating the impact of the adversarial contamination, and we demonstrate the effectiveness of regularization in both real and synthetic data.


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Joshua Agterberg. Youngser Park. Jonathan Larson. Christopher White. Carey E. Priebe. Vince Lyzinski. "Vertex nomination, consistent estimation, and adversarial modification." Electron. J. Statist. 14 (2) 3230 - 3267, 2020.


Received: 1 July 2019; Published: 2020
First available in Project Euclid: 8 September 2020

zbMATH: 1448.62087
MathSciNet: MR4146361
Digital Object Identifier: 10.1214/20-EJS1744

Primary: 62H99

Keywords: adversarial machine learning , networks , Random graphs , statistics , Vertex nomination

Vol.14 • No. 2 • 2020
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