Computing Affine Combinations, Distances, and Correlations for Recursive Partition Functions

TL;DR

This paper introduces efficient algorithms for combining, comparing, and quantifying differences between recursive partition functions, enhancing the analysis of tree-based models like CART and random forests.

Contribution

It presents novel methods for affine combinations, distances, and correlations specifically designed for recursive partition functions, addressing gaps in existing tree analysis techniques.

Findings

Developed fast algorithms for affine combinations of trees

Established methods for measuring distances and correlations between trees

Facilitated systematic comparison of multiple tree models

Abstract

Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a single tree, or methods for systematically quantifying the discrepancy between two trees. Taking advantage of the recursive structure in trees we formulated fast algorithms for computing affine combinations, distances and correlations in a vector subspace of recursive partition functions.