Minimax optimal seriation in polynomial time

TL;DR

This paper introduces a polynomial-time algorithm for the seriation problem that achieves minimax optimal rates under broad conditions, advancing theoretical understanding and practical solutions for recovering hidden orderings from noisy data.

Contribution

It establishes sharp minimax rates under extended conditions and provides the first polynomial-time algorithm that attains these rates for the seriation problem.

Findings

The algorithm achieves minimax optimal rates.

Theoretical analysis extends to broader matrix classes.

Resolves open questions from prior work.

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.