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# Optimality of Belief Propagation for Crowdsourced Classification

*Proceedings of The 33rd International Conference on Machine Learning*, PMLR 48:535-544, 2016.

#### Abstract

Crowdsourcing systems are popular for solving large-scale labelling tasks with low-paid (or even non-paid) workers. We study the problem of recovering the true labels from noisy crowdsourced labels under the popular Dawid-Skene model. To address this inference problem, several algorithms have recently been proposed, but the best known guarantee is still significantly larger than the fundamental limit. We close this gap under a simple but canonical scenario where each worker is assigned at most two tasks. In particular, we introduce a tighter lower bound on the fundamental limit and prove that Belief Propagation (BP) exactly matches this lower bound. The guaranteed optimality of BP is the strongest in the sense that it is information-theoretically impossible for any other algorithm to correctly la- bel a larger fraction of the tasks. In the general setting, when more than two tasks are assigned to each worker, we establish the dominance result on BP that it outperforms other existing algorithms with known provable guarantees. Experimental results suggest that BP is close to optimal for all regimes considered, while existing state-of-the-art algorithms exhibit suboptimal performances.