Dimension Reduction Forests: Local Variable Importance using Structured Random Forests

TL;DR

This paper introduces a novel nonparametric estimator combining random forest kernels with local sufficient dimension reduction to assess variable importance at a local level, enhancing interpretability in personalized applications.

Contribution

It develops a new local variable importance measure using structured random forests and efficient fitting procedures, improving upon existing global importance assessments.

Findings

Significant accuracy improvements over competing methods.

Effective local importance measures demonstrated on real data.

Applicable to personalized medicine and environmental studies.

Abstract

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.