Robust Boosting for Regression Problems
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The gradient boosting algorithm constructs a regression estimator using a linear combination of simple "base learners". In order to obtain a robust non-parametric regression estimator that is scalable to high dimensional problems we propose a robust boosting algorithm based on a two-stage approach, similar to what is done for robust linear regression: we first minimize a robust residual scale estimator, and then improve its efficiency by optimizing a bounded loss function. Unlike previous proposals, our algorithm does not need to compute an ad-hoc residual scale estimator in each step. Since our loss functions are typically non-convex, we propose initializing our algorithm with an L_1 regression tree, which is fast to compute. We also introduce a robust variable importance metric for variable selection that is calculated via a permutation procedure. Through simulated and real data experiments, we compare our method against gradient boosting with squared loss and other robust boosting methods in the literature. With clean data, our method works equally well as gradient boosting with the squared loss. With symmetric and asymmetrically contaminated data, we show that our proposed method outperforms in terms of prediction error and variable selection accuracy.
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