Minimax optimal seriation in polynomial time
Statistics Theory
2025-12-10 v3 Statistics Theory
Abstract
We consider the seriation problem, whose goal is to recover a hidden ordering from a noisy observation of a permuted Robinson matrix. We establish sharp minimax rates under average-Lipschitz conditions that strictly extend the bi-Lipschitz framework of [Giraud et al., 2023]. We further design a polynomial-time algorithm that attains these optimal rates, thereby resolving two open questions raised in [Giraud et al., 2023]. Finally, our analysis extends to a broader class of matrices beyond those generated by exact permutations.
Keywords
Cite
@article{arxiv.2405.08747,
title = {Minimax optimal seriation in polynomial time},
author = {Yann Issartel and Christophe Giraud and Nicolas Verzelen},
journal= {arXiv preprint arXiv:2405.08747},
year = {2025}
}