Random Forest's name hints at a second layer of randomness beyond simple bagging. While bagging averages many trees to reduce variance, Breiman's 2001 design adds feature subsampling at each split, limiting each tree to a random subset of features. This extra randomness targets correlated errors among trees, which averaging alone cannot fully eliminate. The article explains that correlation between tree predictions creates a ceiling for bagging's performance, and feature subsampling mathematically breaks through this barrier. By reducing tree-to-tree correlation, Random Forest achieves lower overall variance and better predictive power. The piece revisits bias‑variance decomposition, emphasizing that bagging reduces variance but not bias, and underscores why Random Forest's random feature selection is essential for optimal ensemble performance.

The mathematical core shows how correlated errors limit bagging's variance reduction, and the experiment validates that feature subsampling indeed lowers correlation, leading to improved model accuracy. This insight reveals Random Forest as an elegant solution to a specific problem: correlated errors that averaging cannot fully address.