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We characterize and study variable importance (VIMP) and pairwise variable associations in binary regression trees. A key component involves the node mean squared error for a quantity we refer to as a maximal subtree. The theory naturally extends from single trees to ensembles of trees and applies to methods like random forests. This is useful because while importance values from random forests are used to screen variables, for example they are used to filter high throughput genomic data in Bioinformatics, very little theory exists about their properties.
Random forest (RF) methodology is one of the most popular machine learning techniques for prediction problems. In this article, we discuss some cases where random forests may suffer and propose a novel generalized RF method, namely regression-enhance
Since their inception in the 1980s, regression trees have been one of the more widely used non-parametric prediction methods. Tree-structured methods yield a histogram reconstruction of the regression surface, where the bins correspond to terminal no
Random forests are one of the most popular machine learning methods due to their accuracy and variable importance assessment. However, random forests only provide variable importance in a global sense. There is an increasing need for such assessments
A new 2-parameter family of central structures in trees, called central forests, is introduced. Miniekas $m$-center problem and McMorriss and Reids central-$k$-tree can be seen as special cases of central forests in trees. A central forest is defined
Bayesian Additive Regression Trees (BART) are non-parametric models that can capture complex exogenous variable effects. In any regression problem, it is often of interest to learn which variables are most active. Variable activity in BART is usually