# FACT: High-Dimensional Random Forests Inference

arXiv: https://arxiv.org/abs/2207.01678 · HTML: https://mlsanity.com/paper/2207.01678/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 48 references that are in the map.
- First posted on arXiv 4 Jul 2022.

## Builds on (most cited first, 17 of 17)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [A Random Forest Guided Tour](https://mlsanity.com/paper/1511.05741/) (2015)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Correlation and variable importance in random forests](https://mlsanity.com/paper/1310.5726/) (2013)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [Large Scale Prediction with Decision Trees](https://mlsanity.com/paper/2104.13881/) (2021)
- [A Debiased MDI Feature Importance Measure for Random Forests](https://mlsanity.com/paper/1906.10845/) (2019)
- [Fast and Powerful Conditional Randomization Testing via Distillation](https://mlsanity.com/paper/2006.03980/) (2020)
- [Trees, forests, and impurity-based variable importance](https://mlsanity.com/paper/2001.04295/) (2020)
- [Predicting the direction of stock market prices using random forest](https://mlsanity.com/paper/1605.00003/) (2016)
- [Estimation and Inference with Trees and Forests in High Dimensions](https://mlsanity.com/paper/2007.03210/) (2020)
- [Conditional Independence Testing in Hilbert Spaces with Applications to Functional Data Analysis](https://mlsanity.com/paper/2101.07108/) (2021)
- [Unbiased variable importance for random forests](https://mlsanity.com/paper/2003.02106/) (2020)
- [MDA for random forests: inconsistency, and a practical solution via the Sobol-MDA](https://mlsanity.com/paper/2102.13347/) (2021)
- [On the power of conditional independence testing under model-X](https://mlsanity.com/paper/2005.05506/) (2020)
- [Nonparametric Feature Selection by Random Forests and Deep Neural Networks](https://mlsanity.com/paper/2201.06821/) (2022)

## Built on by (most cited first, 1 of 1)

- [Analyze Additive and Interaction Effects via Collaborative Trees](https://mlsanity.com/paper/2405.11477/) (2024)

## Abstract (arXiv)

Quantifying the usefulness of individual features in random forests learning can greatly enhance its interpretability. Existing studies have shown that some popularly used feature importance measures for random forests suffer from the bias issue. In addition, there lack comprehensive size and power analyses for most of these existing methods. In this paper, we approach the problem via hypothesis testing, and suggest a framework of the self-normalized feature-residual correlation test (FACT) for evaluating the significance of a given feature in the random forests model with bias-resistance property, where our null hypothesis concerns whether the feature is conditionally independent of the response given all other features. Such an endeavor on random forests inference is empowered by some recent developments on high-dimensional random forests consistency. Under a fairly general high-dimensional nonparametric model setting with dependent features, we formally establish that FACT can provide theoretically justified feature importance test with controlled type I error and enjoy appealing power property. The theoretical results and finite-sample advantages of the newly suggested method are illustrated with several simulation examples and an economic forecasting application.