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Crowdsourcing is a strategy to categorize data through the contribution ofmany individuals. A wide range of theoretical and algorithmic contributions arebased on the model of Dawid and Skene [1]. Recently it was shown in [2,3] that,in certain regimes, belief propagation is asymptotically optimal for datagenerated from the Dawid-Skene model. This paper is motivated by this recentprogress. We analyze the dense limit of the Dawid-Skene model. It is shown thatit belongs to a larger class of low-rank matrix estimation problems for whichit is possible to express the asymptotic, Bayes-optimal, performance in asimple closed form. In the dense limit the mapping to a low-rank matrixestimation problem provides an approximate message passing algorithm thatsolves the problem algorithmically. We identify the regions where the algorithmefficiently computes the Bayes-optimal estimates. Our analysis refines theresults of [2,3] about optimality of message passing algorithms bycharacterizing regions of parameters where these algorithms do not match theBayes-optimal performance. We further study numerically the performance ofapproximate message passing, derived in the dense limit, on sparse instancesand carry out experiments on a real world dataset.

Dense Limit of the Dawid-Skene Model for Crowdsourcing and Regions of Sub-optimality of Message Passing Algorithms