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.

中文翻译：

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回归问题的稳健提升

梯度提升算法使用“基础学习器”的线性组合构建回归预测器。Boosting 还提供了一种获得稳健的非参数回归估计量的方法，这些估计量可扩展到具有许多解释变量的应用程序。鲁棒提升算法基于两阶段方法，类似于鲁棒线性回归：它首先最小化鲁棒残差规模估计器，然后通过优化有界损失函数来改进它。与之前的稳健提升提议不同，这种方法不需要在每次提升迭代中计算临时残差规模估计器。由于这种稳健提升算法中涉及的损失函数通常是非凸的，因此需要一个可靠的初始化步骤，例如 L1 回归树，它的计算速度也很快。还可以通过置换过程计算稳健的变量重要性度量。全面的模拟研究和多项数据分析表明，当不存在非典型观察时，稳健提升方法与具有平方损失的标准梯度提升一样有效。此外，当数据包含异常值时，鲁棒提升估计器在预测误差和变量选择精度方面优于替代方案。