On the Oracle Properties of Bayesian Random Forest for Sparse High-Dimensional Gaussian Regression

Abstract

Random forest (RF) is a widely used data prediction and variable selection technique. However, the variable selection aspect of RF can become unreliable when there are more irrelevant variables than relevant ones. In response, we introduced the Bayesian random forest (BRF) method, specifically designed for high-dimensional datasets with a sparse covariate structure. Our research demonstrates that BRF possesses the oracle property, which means it achieves strong selection consistency without compromising the efficiency or bias.

Keywords

• random forest
• oracle property
• variable selection
• Bayesian analysis
• asymptotic normality