做集成学习或模型部署的团队，SCSB 能帮你把随机森林等 Bagging 模型压缩 96% 且校准更好，直接省推理成本。
本文提出 Simplex-Constrained Sparse Bagging (SCSB)，一种用于后训练压缩和概率校准的数学框架。标准 Bagging 集成（如随机森林、Bagged SVM 等）对所有基估计器赋予均匀投票权重，忽略了它们在不同区域的局部能力差异，导致模型过度自信。SCSB 通过在概率单纯形上最小化袋外损失，将集成剪枝和校准联合优化，并引入凹二次惩罚解决 L1 单纯形悖论（L1 范数在单纯形上为常数，无法直接剪枝）。该方法与模型无关，可实现高达 96% 的集成压缩，带来线性推理加速，同时降低期望校准误差，保持或提升泛化精度。
Simplex-Constrained Sparse Bagging: Transitioning from Uniform Priors to Sparse Posteriors in Ensemble Learning
We present Simplex-Constrained Sparse Bagging (SCSB), a mathematically rigorous framework for post-training compression and probability calibration of bootstrap-based bagging ensembles. Standard bagging ensembles (such as Random Forests, Bagged SVMs, and Bagged Neural Networks) assign uniform voting power to all constituent estimators. However, this naive uniform prior ignores the varying local competence of base estimators and contributes to model overconfidence. We formulate ensemble pruning and calibration as a joint optimization problem over the probability simplex by minimizing the Out-Of-Bag (OOB) loss. To induce sparsity, we address the theoretical "L1-simplex paradox" -- the mathematical reality that the L1 norm is constant on the simplex and fails to prune -- by introducing a concave quadratic penalty. SCSB is model-agnostic and achieves up to 96% ensemble compression, yielding linear inference speedups and superior probability calibration (lowered Expected Calibration Error) while preserving or enhancing generalization accuracy.