2024/12/17 by Nico Föge, Föge, Nico, Lena Schmid +5 · 3 citations
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Probability and Risk Models #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2412.13020
openalex publication_date 2024/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Random Forests have become a widely used tool in machine learning since their introduction in 2001, known for their strong performance in classification and regression tasks. One key feature of Random Forests is the Random Forest Permutation Importance Measure (RFPIM), an internal, non-parametric measure of variable importance. While widely used, theoretical work on RFPIM is sparse, and most research has focused on empirical findings. However, recent progress has been made, such as establishing consistency of the RFPIM, although a mathematical analysis of its asymptotic distribution is still missing. In this paper, we provide a formal proof of a Central Limit Theorem for RFPIM using U-Statistics theory. Our approach deviates from the conventional Random Forest model by assuming a random number of trees and imposing conditions on the regression functions and error terms, which must be bounded and additive, respectively. Our result aims at improving the theoretical understanding of RFPIM rather than conducting comprehensive hypothesis testing. However, our contributions provide a solid foundation and demonstrate the potential for future work to extend to practical applications which we also highlight with a small simulation study.