  The task of aggregating and denoising crowd-labeled data has gained increased
significance with the advent of crowdsourcing platforms and massive datasets.
We propose a permutation-based model for crowd labeled data that is a
significant generalization of the classical Dawid-Skene model, and introduce a
new error metric by which to compare different estimators. We derive global
minimax rates for the permutation-based model that are sharp up to logarithmic
factors, and match the minimax lower bounds derived under the simpler
Dawid-Skene model. We then design two computationally-efficient estimators: the
WAN estimator for the setting where the ordering of workers in terms of their
abilities is approximately known, and the OBI-WAN estimator where that is not
known. For each of these estimators, we provide non-asymptotic bounds on their
performance. We conduct synthetic simulations and experiments on real-world
crowdsourcing data, and the experimental results corroborate our theoretical
findings.
