FACT: High-Dimensional Random Forests Inference

TL;DR

This paper introduces FACT, a bias-resistant hypothesis testing framework for assessing feature importance in high-dimensional random forests, supported by theoretical guarantees and demonstrated through simulations and an economic forecasting case.

Contribution

It proposes a novel self-normalized feature-residual correlation test (FACT) for unbiased feature significance testing in high-dimensional random forests.

Findings

FACT controls type I error effectively.

FACT demonstrates high power in simulations.

Application to economic data shows practical utility.

Abstract

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.