Abstract
Most boosting regression algorithms use the weighted average of base regressors as their final regressor. In this paper we analyze the choice of the weighted median. We propose a general boosting algorithm based on this approach. We prove boosting-type convergence of the algorithm and give clear conditions for the convergence of the robust training error. The algorithm recovers $\textsc{AdaBoost}$ and $\textsc{AdaBoost}_\varrho$ as special cases. For boosting confidence-rated predictions, it leads to a new approach that outputs a different decision and interprets robustness in a different manner than the approach based on the weighted average. In the general, non-binary case we suggest practical strategies based on the analysis of the algorithm and experiments.
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