# Exact Finite-Sample Variance Decomposition of Subagging: A Spectral Filtering Perspective

arXiv: https://arxiv.org/abs/2604.10469 · HTML: https://mlsanity.com/paper/2604.10469/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 44 references that are in the map.
- First posted on arXiv 12 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Understanding Random Forests: From Theory to Practice](https://mlsanity.com/paper/1407.7502/) (2014)
- [Explaining the Success of AdaBoost and Random Forests as Interpolating Classifiers](https://mlsanity.com/paper/1504.07676/) (2015)
- [Why do Random Forests Work? Understanding Tree Ensembles as Self-Regularizing Adaptive Smoothers](https://mlsanity.com/paper/2402.01502/) (2024)
- [On Variance Estimation of Random Forests with Infinite-Order U-statistics](https://mlsanity.com/paper/2202.09008/) (2022)
- [Asymptotic Theory for Random Forests](https://mlsanity.com/paper/1405.0352/) (2014)
- [Random Forests as Statistical Procedures: Design, Variance, and Dependence](https://mlsanity.com/paper/2602.13104/) (2026)

## Abstract (arXiv)

Standard resampling ratios (e.g., α ≈ 0.632) are widely used as default baselines in ensemble learning for three decades. However, how these ratios interact with a base learner's intrinsic functional complexity in finite samples lacks a exact mathematical characterization. We leverage the Hoeffding-ANOVA decomposition to derive the first exact, finite-sample variance decomposition for subagging, applicable to any symmetric base learner without requiring asymptotic limits or smoothness assumptions. We establish that subagging operates as a deterministic low-pass spectral filter: it preserves low-order structural signals while attenuating c-th order interaction variance by a geometric factor approaching αc. This decoupling reveals why default baselines often under-regularize high-capacity interpolators, which instead require smaller α to exponentially suppress spurious high-order noise. To operationalize these insights, we propose a complexity-guided adaptive subsampling algorithm, empirically demonstrating that dynamically calibrating α to the learner's complexity spectrum consistently improves generalization over static baselines.