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.

翻译：随机森林是因其准确性和可变重要性评估而最受欢迎的机械学习方法之一。然而,随机森林仅具有全球意义的不同重要性。由于个人化医学、决策和生物信息学方面的应用,越来越需要在地方一级进行这种评估。我们提出了一个新的非参数估计器,将灵活的随机森林内核与本地足够尺寸的减少相配,以适应回归函数的当地结构。这使我们能够在每个预测点估计一个有意义的方向性地方变量重要性指标。我们制定了一个计算高效的适应程序,并为分离方向的恢复提供了充分的条件。我们展示了我们对模拟和实际回归问题相竞争方法的拟议估算器的显著准确性。最后,我们采用了在中国北京收集的季节性微粒物质集中数据的拟议方法,这些数据产生了有意义的地方重要性措施。这里介绍的方法见于Dr Fornor Python 软件包。