  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.
