  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.
