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The diversity forest algorithm is an alternative candidate node split sampling scheme that makes innovative complex split procedures in random forests possible. While conventional univariable, binary splitting suffices for obtaining strong predictive performance, new complex split procedures can help tackling practically important issues. For example, interactions between features can be exploited effectively by bivariable splitting. With diversity forests, each split is selected from a candidate split set that is sampled in the following way: for    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$l = 1, \dots , {nsplits}$$\end{document}    l  =  1  ,  ⋯  ,   nsplits: (1) sample one split problem; (2) sample a single or few splits from the split problem sampled in (1) and add this or these splits to the candidate split set. The split problems are specifically structured collections of splits that depend on the respective split procedure considered. This sampling scheme makes innovative complex split procedures computationally tangible while avoiding overfitting. Important general properties of the diversity forest algorithm are evaluated empirically using univariable, binary splitting. Based on 220 data sets with binary outcomes, diversity forests are compared with conventional random forests and random forests using extremely randomized trees. It is seen that the split sampling scheme of diversity forests does not impair the predictive performance of random forests and that the performance is quite robust with regard to the specified  nsplits  value. The recently developed interaction forests are the first diversity forest method that uses a complex split procedure. Interaction forests allow modeling and detecting interactions between features effectively. Further potential complex split procedures are discussed as an outlook.   Supplementary Information  The online version contains supplementary material available at 10.1007/s42979-021-00920-1.

Diversity Forests: Using Split Sampling to Enable Innovative Complex Split Procedures in Random Forests