Iterative Bayesian Learning for Crowdsourced Regression
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Crowdsourcing platforms emerged as popular venues for purchasing human intelligence at low cost for large volumes of tasks. As many low-paid workers are prone to give noisy answers, one of the fundamental questions is how to identify more reliable workers and exploit this heterogeneity to infer the true answers accurately. Despite significant research efforts for classification tasks with discrete answers, little attention has been paid to regression tasks with continuous answers. The popular Dawid-Skene model for discrete answers has the algorithmic and mathematical simplicity in relation to low-rank structures. But it does not generalize for continuous valued answers. To this end, we introduce a new probabilistic model for crowdsourced regression capturing the heterogeneity of the workers, generalizing the Dawid-Skene model to the continuous domain. We design a message-passing algorithm for Bayesian inference inspired by the popular belief propagation algorithm. We showcase its performance first by proving that it achieves a near optimal mean squared error by comparing it to an oracle estimator. Asymptotically, we can provide a tighter analysis showing that the proposed algorithm achieves the exact optimal performance. We next show synthetic experiments confirming our theoretical predictions. As a practical application, we further emulate a crowdsourcing system reproducing PASCAL visual object classes datasets and show that de-noising the crowdsourced data from the proposed scheme can significantly improve the performance for the vision task.
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