改进在线决策树的分裂选择，让每次判断都统计有效。
Correcting Split Selection in Online Decision Trees via Anytime-Valid Inference
- 用随时有效的统计推断替代传统方法，确保分裂判断可靠
- 在非平稳数据流中错误分裂概率可控，且模型更紧凑
- 适合需要高可靠性在线学习的场景，如金融、工业监控
基于袋装法的集成模型，尤其是自适应随机森林，是处理数据流的强性能方法。这些方法普遍依赖霍夫丁树作为基学习器，通过集中不等式判断候选分裂是否显著优于其他选项，实现增量式树生长。然而现有方法缺乏严格的统计保证：分析依赖于固定样本的浓度界，而实际分裂决策使用数据依赖的停止规则，导致统计保证失效，错误分裂概率可能趋近于1。本文提出基于随时有效推断的系统性替代方案。该方法在任意数据流（包括非平稳环境）下可保证错误分裂的控制；在具备预测优势时具有有限承诺时间；在平稳独立同分布数据下，风险单调递减，每一步分裂均带来严格提升。实验评估了独立树及在自适应随机森林中的应用，结果表明新方法性能更优，同时生成的树显著更小。
原文摘要 · Abstract (English)
Bagging-based ensembles, most notably Adaptive Random Forests, are among the strongest performers for learning from data streams. A common denominator across these methods is their reliance on Hoeffding Trees as base learners, which grow decision trees incrementally by testing whether a candidate split is significantly better than its alternatives using concentration inequalities. Despite their empirical success, existing variants lack valid statistical guarantees. Current analyses rely on fixed-sample concentration bounds, while split decisions are made using data-dependent stopping rules, which invalidates their guarantees and can drive the probabilty of incorrect splits to one. We introduce a principled alternative based on anytime-valid inference. Our method provides: (i) anytime-valid control of false splits under arbitrary data streams, including non-stationary settings; (ii) finite commitment time under a predictive advantage; and (iii) under stationary i.i.d. data, risk is monotone decreasing and strictly improves at every split. Empirically, we evaluate both standalone trees and their use within Adaptive Random Forests on non-stationary streams. Our method improves performance while producing substantially smaller trees.
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