Robust Learning from Bites

Many robust statistical procedures have two drawbacks. Firstly, they are computer-intensive such that they can hardly be used for massive data sets. Secondly, robust confidence intervals for the estimated parameters or robust predictions according to the fitted models are often unknown. Here, we propose a general method to overcome these problems of robust estimation in the context of huge data sets. The method is scalable to the memory of the computer, can be distributed on several processors if available, and can help to reduce the computation time substantially. The method additionally offers distribution-free confidence intervals for the median of the predictions. The method is illustrated for two situations: robust estimation in linear regression and kernel logistic regression from statistical machine learning.