Local Linear Forests

Random forests are a powerful method for nonparametric regression, but are limited in their ability to fit smooth signals. Taking the perspective of random forests as an adaptive kernel method, we pair the forest kernel with a local linear regression adjustment to better capture smoothness. The resulting procedure, local linear forests, enables us to improve on asymptotic rates of convergence for random forests with smooth signals, and provides substantial gains in accuracy on both real and simulated data. We prove a central limit theorem valid under regularity conditions on the forest and smoothness constraints, and propose a computationally efficient construction for confidence intervals. Moving to a causal inference application, we discuss the merits of local regression adjustments for heterogeneous treatment effect estimation, and give an example on a dataset exploring the effect word choice has on attitudes to the social safety net. Last, we include simulation results on real and generated data. A software implementation is available in the R package grf. Supplementary materials for this article are available online.

随机森林作为一种强大的非参数回归方法，在拟合平滑信号方面存在局限性。从随机森林作为自适应核方法的视角出发，我们结合森林核与局部线性回归调整，以期更有效地捕捉平滑性。由此产生的局部线性森林方法，使我们能够提升随机森林在平滑信号上的渐近收敛速度，并在真实和模拟数据集上显著提高准确性。我们在森林的常规性条件和平滑性约束下，证明了中心极限定理的有效性，并提出了一个计算高效的置信区间构建方法。转向因果推断应用，我们探讨了局部回归调整在异质处理效应估计中的优势，并在一个探究词汇选择对社会安全网态度影响的样本数据集上给出了实例。最后，我们包括了真实和生成数据上的模拟结果。此软件实现可在R语言的grf包中找到。本文的补充材料可在网上获取。