Unsupervised Ensemble Regression
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Consider a regression problem where there is no labeled data and the only observations are the predictions f_i(x_j) of m experts f_i over many samples x_j. With no knowledge on the accuracy of the experts, is it still possible to accurately estimate the unknown responses y_j? Can one still detect the least or most accurate experts? In this work we propose a framework to study these questions, based on the assumption that the m experts have uncorrelated deviations from the optimal predictor. Assuming the first two moments of the response are known, we develop methods to detect the best and worst regressors, and derive U-PCR, a novel principal components approach for unsupervised ensemble regression. We provide theoretical support for U-PCR and illustrate its improved accuracy over the ensemble mean and median on a variety of regression problems.
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