众包问题中的最优置换估计
Optimal Permutation Estimation in Crowd-Sourcing problems
摘要：
出于众包应用程序，我们考虑一个模型，其中我们有部分观察到一个二元保序n × d矩阵与一个未知的置换$π$ * 作用于其行。专注于恢复置换$π$ * 和估计未知矩阵的孪生问题，我们介绍了一个多项式时间的过程，实现这两个问题的极大极小风险，这对于所有可能的值n，d，和所有可能的采样努力。一路上，我们建立，在某些制度，恢复未知的置换$π$ * 是相当简单的估计矩阵。
英文摘要：
Motivated by crowd-sourcing applications, we consider a model where we have partial observations from a bivariate isotonic n x d matrix with an unknown permutation $π$ * acting on its rows. Focusing on the twin problems of recovering the permutation $π$ * and estimating the unknown matrix, we introduce a polynomial-time procedure achieving the minimax risk for these two problems, this for all possible values of n, d, and all possible sampling efforts. Along the way, we establish that, in some regimes, recovering the unknown permutation $π$ * is considerably simpler than estimating the matrix.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
