# Dimension Reduction Forests: Local Variable Importance using Structured Random Forests

arXiv: https://arxiv.org/abs/2103.13233 · HTML: https://mlsanity.com/paper/2103.13233/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2021.

## Built on by (most cited first, 3 of 3)

- [Statistical Advantages of Oblique Randomized Decision Trees and Forests](https://mlsanity.com/paper/2407.02458/) (2024)
- [TrIM: Transformed Iterative Mondrian Forests for Gradient-based Dimension Reduction and High-Dimensional Regression](https://mlsanity.com/paper/2407.09964/) (2024)
- [WildWood: a new Random Forest algorithm](https://mlsanity.com/paper/2109.08010/) (2021)

## Abstract (arXiv)

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 at a local level, motivated by applications in personalized medicine, policy-making, and bioinformatics. We propose a new nonparametric estimator that pairs the flexible random forest kernel with local sufficient dimension reduction to adapt to a regression function's local structure. This allows us to estimate a meaningful directional local variable importance measure at each prediction point. We develop a computationally efficient fitting procedure and provide sufficient conditions for the recovery of the splitting directions. We demonstrate significant accuracy gains of our proposed estimator over competing methods on simulated and real regression problems. Finally, we apply the proposed method to seasonal particulate matter concentration data collected in Beijing, China, which yields meaningful local importance measures. The methods presented here are available in the drforest Python package.