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Sharp threshold for alignment of graph databases with Gaussian weights

Luca Ganassali
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Abstract

We study the fundamental limits for reconstruction in weighted graph (or matrix) database alignment. We consider a model of two graphs $G, G',$ where $G$ and $G'$ have correlated Gaussian edge weights, and then $G$ is relabeled according to a random uniform permutation. We prove that there is a sharp information-theoretic threshold for exact recovery of the planted permutation. This threshold is the same as the one obtained for detection in a recent work by Y. Wu, J. Xu and S. Yu: in other words, for Gaussian weighted graph alignment, the problem of reconstruction is not more difficult than that of detection. The study is based on the analysis of the MAP estimator, and proofs rely on proper use of the correlation structure of energies of permutations.
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Dates and versions

hal-03139777 , version 1 (02-11-2021)

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Luca Ganassali. Sharp threshold for alignment of graph databases with Gaussian weights. MSML21 (Mathematical and Scientific Machine Learning), Aug 2021, Lausanne, Switzerland. ⟨hal-03139777⟩
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