# Linear Aggregation in Tree-based Estimators

arXiv: https://arxiv.org/abs/1906.06463 · HTML: https://mlsanity.com/paper/1906.06463/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2019.

## Built on by (most cited first, 5 of 5)

- [A cautionary tale on fitting decision trees to data from additive models: generalization lower bounds](https://mlsanity.com/paper/2110.09626/) (2021)
- [SynthTree: Co-supervised Local Model Synthesis for Explainable Prediction](https://mlsanity.com/paper/2406.10962/) (2024)
- [Estimating the age-conditioned average treatment effects curves: An application for assessing load-management strategies in the NBA](https://mlsanity.com/paper/2402.12400/) (2024)
- [SMART: A Flexible Approach to Regression using Spline-Based Multivariate Adaptive Regression Trees](https://mlsanity.com/paper/2410.05597/) (2024)
- [Oblique Bayesian additive regression trees](https://mlsanity.com/paper/2411.08849/) (2024)

## Abstract (arXiv)

Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study regression trees and random forests with linear aggregation functions. We introduce a new algorithm that finds the best axis-aligned split to fit linear aggregation functions on the corresponding nodes, and we offer a quasilinear time implementation. We demonstrate the algorithm's favorable performance on real-world benchmarks and in an extensive simulation study, and we demonstrate its improved interpretability using a large get-out-the-vote experiment. We provide an open-source software package that implements several tree-based estimators with linear aggregation functions.