Robust random graph matching in dense graphs via vector approximate message passing

• URL: http://arxiv.org/abs/2412.16457v1
• Date: Sat, 21 Dec 2024 03:15:38 GMT
• Title: Robust random graph matching in dense graphs via vector approximate message passing
• Authors: Zhangsong Li,
• Abstract summary: We focus on the matching recovery problem between a pair of correlated Gaussian Wigner matrices with a latent correspondence. Our algorithm is the first efficient random graph matching type algorithm that is robust under any adversarial perturbations of $n1-o(1)$ size.
• Score: 0.0
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• Abstract: In this paper, we focus on the matching recovery problem between a pair of correlated Gaussian Wigner matrices with a latent vertex correspondence. We are particularly interested in a robust version of this problem such that our observation is a perturbed input $(A+E,B+F)$ where $(A,B)$ is a pair of correlated Gaussian Wigner matrices and $E,F$ are adversarially chosen matrices supported on an unknown $\epsilon n * \epsilon n$ principle minor of $A,B$, respectively. We propose a vector-approximate message passing (vector-AMP) algorithm that succeeds in polynomial time as long as the correlation $\rho$ between $(A,B)$ is a non-vanishing constant and $\epsilon = o\big( \tfrac{1}{(\log n)^{20}} \big)$. The main methodological inputs for our result are the iterative random graph matching algorithm proposed in \cite{DL22+, DL23+} and the spectral cleaning procedure proposed in \cite{IS24+}. To the best of our knowledge, our algorithm is the first efficient random graph matching type algorithm that is robust under any adversarial perturbations of $n^{1-o(1)}$ size.

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