Phase Transition in Convex Relaxations for Graph Alignment
We study the graph alignment problem for correlated Gaussian Orthogonal Ensemble (GOE) matrices, where the goal is to recover a hidden vertex permutation given two correlated symmetric Gaussian matrices $(A, B)$ with correlation $1/\sqrt{1+σ^2}$. While the maximum likelihood estimator is information-theoretically optimal, its computation, which reduces to a quadratic assignment problem, is intractable. Motivated by this, we analyze convex relaxations based on minimizing $\|AX - XB\|_F$ over the set of doubly stochastic matrices and the unit hypercube. We show that when the correlation parameter satisfies $σ= o(n^{-1/2}/\log^4 n)$, the solution of either relaxation $(X^\star)$ concentrates...
| Authors | Laurent Massoulié, Sushil Mahavir Varma, Louis Vassaux et al. |
|---|---|
| Primary category | stat.ML |
| Published | 14 June 2026 |
| Last updated at source | 14 June 2026 |
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