# A Comparison of Resampling and Recursive Partitioning Methods in Random Forest for Estimating the Asymptotic Variance Using the Infinitesimal Jackknife

## TL;DR

This paper evaluates the effectiveness of the infinitesimal jackknife in estimating variance in random forests, finding that using conditional inference trees and subsampling improves accuracy, and introduces an R package for these methods.

## Contribution

It demonstrates the improved applicability of the infinitesimal jackknife with alternative resampling methods and base learners in random forests, and provides an open-source implementation.

## Key findings

- CI trees and subsampling improve variance estimation accuracy
- The proposed methods outperform traditional bootstrap and CART trees
- Open-source R package available for implementation

## Abstract

The infinitesimal jackknife (IJ) has recently been applied to the random forest to estimate its prediction variance. These theorems were verified under a traditional random forest framework which uses classification and regression trees (CART) and bootstrap resampling. However, random forests using conditional inference (CI) trees and subsampling have been found to be not prone to variable selection bias. Here, we conduct simulation experiments using a novel approach to explore the applicability of the IJ to random forests using variations on the resampling method and base learner. Test data points were simulated and each trained using random forest on one hundred simulated training data sets using different combinations of resampling and base learners. Using CI trees instead of traditional CART trees as well as using subsampling instead of bootstrap sampling resulted in a much more accurate estimation of prediction variance when using the IJ. The random forest variations here have been incorporated into an open source software package for the R programming language.