Local Linear Forests

TL;DR

This paper introduces local linear forests, a method combining random forests with local linear regression to better capture smooth signals, improving accuracy and inference in non-parametric regression and causal effect estimation.

Contribution

It proposes a novel local linear forest method that enhances random forests with a local linear adjustment, improving convergence rates and predictive accuracy for smooth signals.

Findings

Improved asymptotic convergence rates for smooth signals.

Enhanced predictive accuracy on real and simulated data.

A computationally efficient method for confidence interval construction.

Abstract

Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. 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.