Revisiting Stein's Paradox: Multi-Task Averaging

We present a multi-task learning approach to jointly estimate the means of multiple independent distributions from samples. The proposed multi-task averaging (MTA) algorithm results in a convex combination of the individual task's sample averages We derive the optimal amount of regularization for the two task case for the minimum risk estimator and a minimax estimator, and show that the optimal amount of regularization can be practically estimated without cross-validation. We extend the practical estimators to an arbitrary number of tasks. Simulations and real data experiments demonstrate the advantage of the proposed MTA estimators over standard averaging and James-Stein estimation.