Random Forests as Statistical Procedures: Design, Variance, and Dependence
Nathaniel S. O'Connell
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Abstract
Random forests are widely used prediction procedures, yet are typically described algorithmically rather than as statistical designs acting on a fixed set of covariates. We develop a finite-sample, design-based formulation of random forests in which each tree is an explicit randomized conditional regression function. This perspective yields an exact variance identity for the forest predictor that separates finite-aggregation variability from a structural dependence term that persists even under infinite aggregation. We further decompose both single-tree dispersion and inter-tree covariance using the laws of total variance and covariance, isolating two fundamental design mechanisms-reuse of training observations and alignment of data-adaptive partitions. These mechanisms induce a strict covariance floor, demonstrating that predictive variability cannot be eliminated by increasing the number of trees alone. The resulting framework clarifies how resampling, feature-level randomization, and split selection govern resolution, tree variability, and dependence, and establishes random forests as explicit finite-sample statistical designs whose behavior is determined by their underlying randomized construction.引用本文复制引用
Nathaniel S. O'Connell.Random Forests as Statistical Procedures: Design, Variance, and Dependence[EB/OL].(2026-02-17)[2026-02-19].https://arxiv.org/abs/2602.13104.学科分类
计算技术、计算机技术
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