Optimal Permutation Estimation in CrowdSourcing problems
Emmanuel Pilliat, Alexandra Carpentier, Nicolas Verzelen
The Annals of Statistics · 2023 · Volume 51 · Issue 3
Abstract
Motivated by crowdsourcing applications, we consider a model where we have partial observations from a bivariate isotonic n×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.
Keywords
62C20, Bi-isotonic matrices, ranking, sub-Gaussian noise
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