Alternative stopping rules to limit tree expansion for random forest models

Random forests are a popular type of machine learning model, which are relatively robust to overfitting, unlike some other machine learning models, and adequately capture non-linear relationships between an outcome of interest and multiple independent variables. There are relatively few adjustable hyperparameters in the standard random forest models, among them the minimum size of the terminal nodes on each tree. The usual stopping rule, as proposed by Breiman, stops tree expansion by limiting the size of the parent nodes, so that a node cannot be split if it has less than a specified number of observations. Recently an alternative stopping criterion has been proposed, stopping tree expansion so that all terminal nodes have at least a minimum number of observations. The present paper proposes three generalisations of this idea, limiting the growth in regression random forests, based on the variance, range, or inter-centile range. The new approaches are applied to diabetes data obtained from the National Health and Nutrition Examination Survey and four other datasets (Tasmanian Abalone data, Boston Housing crime rate data, Los Angeles ozone concentration data, MIT servo data). Empirical analysis presented herein demonstrate that the new stopping rules yield competitive mean square prediction error to standard random forest models. In general, use of the intercentile range statistic to control tree expansion yields much less variation in mean square prediction error, and mean square prediction error is also closer to the optimal. The Fortran code developed is provided in the Supplementary Material.