  Gradient boosting algorithms construct a regression predictor using a linear
combination of ``base learners''. Boosting also offers an approach to obtaining
robust non-parametric regression estimators that are scalable to applications
with many explanatory variables. The robust boosting algorithm is based on a
two-stage approach, similar to what is done for robust linear regression: it
first minimizes a robust residual scale estimator, and then improves it by
optimizing a bounded loss function. Unlike previous robust boosting proposals
this approach does not require computing an ad-hoc residual scale estimator in
each boosting iteration. Since the loss functions involved in this robust
boosting algorithm are typically non-convex, a reliable initialization step is
required, such as an L1 regression tree, which is also fast to compute. A
robust variable importance measure can also be calculated via a permutation
procedure. Thorough simulation studies and several data analyses show that,
when no atypical observations are present, the robust boosting approach works
as well as the standard gradient boosting with a squared loss. Furthermore,
when the data contain outliers, the robust boosting estimator outperforms the
alternatives in terms of prediction error and variable selection accuracy.
