Journal
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
Volume 30, Issue 2, Pages 503-517Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/10618600.2020.1831930
Keywords
Asymptotic normality; Heterogeneous treatment effect; Smoothing and nonparametric regression
Categories
Funding
- DoD, Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship [32 CFR 168a]
- Sloan Foundation
- ONR [N00014-17-1-2131]
- NSF [DMS-1916163]
- Facebook Faculty Award
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Local linear forests improve the convergence rates of random forests with smooth signals by combining forest kernel with local linear regression adjustment. This method provides substantial gains in accuracy on both real and simulated data. The technique also offers a computationally efficient construction for confidence intervals and can be applied to causal inference applications.
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. for this article are available online.
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