We consider the statistical seriation problem, where the statistician seeks to recover a hidden ordering from a noisy observation of a permuted Robinson matrix. In this paper, we tightly characterize the minimax rate for this problem of matrix reordering when the Robinson matrix is bi-Lipschitz, and we also provide a polynomial time algorithm achieving this rate; thereby answering two open questions of [Giraud et al., 2021]. Our analysis further extends to broader classes of similarity matrices.

翻译：本文考虑统计排序问题，其中统计学家需从带噪声的置换罗宾逊矩阵观测中恢复隐藏顺序。我们严格刻画了当罗宾逊矩阵为双利普希茨时矩阵重排问题的极小化最优率，并提出了达到该最优率的多项式时间算法；由此回答了[Giraud等，2021]中两个开放性问题。我们的分析进一步推广至更广泛的相似矩阵类别。