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In many machine learning applications, crowdsourcing has become the primarymeans for label collection. In this paper, we study the optimal error rate foraggregating labels provided by a set of non-expert workers. Under the classicDawid-Skene model, we establish matching upper and lower bounds with an exactexponent $mI(\pi)$ in which $m$ is the number of workers and $I(\pi)$ theaverage Chernoff information that characterizes the workers' collectiveability. Such an exact characterization of the error exponent allows us tostate a precise sample size requirement$m>\frac{1}{I(\pi)}\log\frac{1}{\epsilon}$ in order to achieve an $\epsilon$misclassification error. In addition, our results imply the optimality ofvarious EM algorithms for crowdsourcing initialized by consistent estimators.

Exact Exponent in Optimal Rates for Crowdsourcing