Quantile Regression Forests

Abstract Random Forests were introduced as a Machine Learning tool in Breiman (2001) and have since proven to be very popular and powerful for high-dimensional regression and classification. For regression, Random Forests give an accurate approximation of the conditional mean of a response variable. It is shown here that Random Forests provide information about the full conditional distribution of the response variable, not only about the conditional mean. Conditional quantiles can be inferred with Quantile Regression Forests, a generalisation of Random Forests. Quantile Regression Forests give a non-parametric and accurate way of estimating conditional quantiles for high-dimensional predictor variables. The algorithm is shown to be consistent. Numerical examples suggest that the algorithm is competitive in terms of predictive power.