Dense Limit of the Dawid-Skene Model for Crowdsourcing and Regions of Sub-optimality of Message Passing Algorithms
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Crowdsourcing is a strategy to categorize data through the contribution of many individuals. A wide range of theoretical and algorithmic contributions are based on the model of Dawid and Skene DawidSkene79. Recently it was shown in ok16,ok2016optimal that, in certain regimes, belief propagation is asymptotically optimal for data generated from the Dawid-Skene model. This paper is motivated by this recent progress. We analyze the dense limit of the Dawid-Skene model. It is shown that it belongs to a larger class of low-rank matrix estimation problems for which it is possible to express the asymptotic, Bayes-optimal, performance in a simple closed form. In the dense limit the mapping to a low-rank matrix estimation problem provides an approximate message passing algorithm that solves the problem algorithmically. We identify the regions where the algorithm efficiently computes the Bayes-optimal estimates. Our analysis refines the results of ok16,ok2016optimal about optimality of message passing algorithms by characterizing regions of parameters where these algorithms do not match the Bayes-optimal performance. We further study numerically the performance of approximate message passing, derived in the dense limit, on sparse instances and carry out experiments on a real world dataset.
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