The aggregation and denoising of crowd labeled data is a task that has gained increased significance with the advent of crowdsourcing platforms and massive datasets. In this paper, we propose a permutation-based model for crowd labeled data that is a significant generalization of the common Dawid-Skene model, and introduce a new error metric by which to compare different estimators. Working in a high-dimensional non-asymptotic framework that allows both the number of workers and tasks to scale, we derive optimal rates of convergence for the permutation-based model. We show that the permutation-based model offers significant robustness in estimation due to its richness, while surprisingly incurring only a small additional statistical penalty as compared to the Dawid-Skene model. Finally, we propose a computationally-efficient method, called the OBI-WAN estimator, that is uniformly optimal over a class intermediate between the permutation-based and the Dawid-Skene models, and is uniformly consistent over the entire permutation-based model class. In contrast, the guarantees for estimators available in prior literature are sub-optimal over the original Dawid-Skene model.
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