Emergent Mind
Matching recovery threshold for correlated random graphs
(2205.14650)
Published May 29, 2022
in
math.ST
,
math.PR
,
stat.ML
,
and
stat.TH
Abstract
For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}. When $p = n{-\alpha+o(1)}$ for $\alpha\in (0, 1]$, we establish a sharp information-theoretic threshold for whether it is possible to correctly match a positive fraction of vertices. Our result sharpens a constant factor in a recent work by Wu, Xu and Yu.
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