Label Correction of Crowdsourced Noisy Annotations with an Instance-Dependent Noise Transition Model

The predictive ability of supervised learning algorithms hinges on the quality of annotated examples, whose labels often come from multiple crowdsourced annotators with diverse expertise. To aggregate noisy crowdsourced annotations, many existing methods employ an annotator-specific instance-independent noise transition matrix to characterize the labeling skills of each annotator. Learning an instance-dependent noise transition model, however, is challenging and remains relatively less explored. To address this problem, in this paper, we formulate the noise transition model in a Bayesian framework and subsequently design a new label correction algorithm. Specifically, we approximate the instance-dependent noise transition matrices using a Bayesian network with a hierarchical spike and slab prior. To theoretically characterize the distance between the noise transition model and the true instance-dependent noise transition matrix, we provide a posterior-concentration theorem that ensures the posterior consistency in terms of the Hellinger distance. We further formulate the label correction process as a hypothesis testing problem and propose a novel algorithm to infer the true label from the noisy annotations based on the pairwise likelihood ratio test. Moreover, we establish an information-theoretic bound on the Bayes error for the proposed method. We validate the effectiveness of our approach through experiments on benchmark and real-world datasets.