Robust Regression Random Forests by Small and Noisy Training Data

Abstract

A regression random forest model taking into account imprecision of the decision tree estimates is proposed. The imprecision stems from conditions of small or noisy training data which may take place in many applications. In fact, a meta-model is proposed to train and to compute optimal weights assigned to decision trees, which control the imprecision in order to get the robust random forest estimates. The imprecision of the tree estimations is defined by means of interval models, for example, by using confidence intervals. The weights are computed by solving a standard quadratic optimization problem with linear constraints. Numerical examples illustrate the proposed robust model which provides outperforming results for noisy and small data in comparison with the standard random forest.