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

• URL: http://arxiv.org/abs/2604.10469v1
• Date: Sun, 12 Apr 2026 05:47:41 GMT
• Title: Exact Finite-Sample Variance Decomposition of Subagging: A Spectral Filtering Perspective
• Abstract summary: We use the Hoeffding-ANOVA decomposition to derive the first exact, finite-sample variance decomposition for subagging.<n>We show that subagging preserves low-order structural signals while atten $c$-th order interaction variance by a geometric factor approaching $c$.<n>This decoupling reveals why default baselines often under-regularize high-capacity interpolators, which instead require smaller $$ to exponentially suppress spurious high-order noise.
• Score: 17.68593329351594
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Standard resampling ratios (e.g., $α\approx 0.632$) 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 $α^c$. 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.

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