Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating an unknown matrix in this class, based on noisy observations of (possibly, a subset of) its entries. We design and analyze polynomial-time algorithms that improve upon the state of the art in two distinct metrics, showing, in particular, that minimax optimal, computationally efficient estimation is achievable in certain settings. Along the way, we prove matching upper and lower bounds on the minimax radii of certain cone testing problems, which may be of independent interest.

中文翻译：

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对未知排列的二元等渗矩阵的最优估计

许多应用程序，包括秩聚合、人群标记和图形估计，可以根据二元等渗矩阵建模，未知排列作用于其行和/或列。我们考虑基于对其条目（可能是其子集）的噪声观察来估计此类中的未知矩阵的问题。我们设计和分析了多项式时间算法，这些算法在两个不同的指标上改进了现有技术，特别是表明在某些设置下可以实现极小极大优化、计算效率高的估计。在此过程中，我们证明了匹配某些锥体测试问题的极大极小半径的上限和下限，这可能是独立的兴趣。