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arXiv · 2405.08747

Minimax optimal seriation in polynomial time

Yann Issartel·Christophe Giraud·Nicolas Verzelen
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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.

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Yann Issartel, Christophe Giraud, Nicolas Verzelen. 2024-05-14. Minimax optimal seriation in polynomial time. https://arxiv.org/abs/2405.08747

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