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arXiv · 1803.04924

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

Christian Schmidt·Lenka Zdeborová
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Abstract

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 [1]. Recently it was shown in [2,3] 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 [2,3] 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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BibTeXRIS

Christian Schmidt, Lenka Zdeborová. 2018-03-15. Dense Limit of the Dawid-Skene Model for Crowdsourcing and Regions of Sub-optimality of Message Passing Algorithms. https://doi.org/10.1088/1751-8121%2Fab757f

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