Crowdsourcing Regression: A Spectral Approach

Merging the predictions of multiple experts is a frequent task. When ground-truth response values are available, this merging is often based on the estimated accuracies of the experts. In various applications, however, the only available information are the experts' predictions on unlabeled test data, which do not allow to directly estimate their accuracies. Moreover, simple merging schemes such as majority voting in classification or the ensemble mean or median in regression, are clearly sub-optimal when some experts are more accurate than others. Focusing on regression tasks, in this work we propose U-PCR, a framework for unsupervised ensemble regression. Specifically, we develop spectral-based methods that under mild assumptions and in the absence of ground truth data, are able to estimate the mean squared error of the different experts and combine their predictions to a more accurate meta-learner. We provide theoretical support for U-PCR as well as empirical evidence for the validity of its underlying assumptions. On a variety of regression problems, we illustrate the improved accuracy of U-PCR over various unsupervised merging strategies. Finally, we also illustrate its applicability to unsupervised multi-class ensemble learning.