Robust Boosting for Regression Problems

• URL: http://arxiv.org/abs/2002.02054v2
• Date: Fri, 7 Aug 2020 21:09:17 GMT
• Title: Robust Boosting for Regression Problems
• Authors: Xiaomeng Ju, Mat\'ias Salibi\'an-Barrera
• Abstract summary: Gradient boosting algorithms construct a regression predictor using a linear combination of base learners'' The robust boosting algorithm is based on a two-stage approach, similar to boosting is done for robust linear regression. When no atypical observations are present, the robust boosting approach works as well as a standard gradient boosting with a squared loss.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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