提出可自适应划分不确定区间的三元决策树，提升预测可靠性。
Ternary Decision Trees with Locally-Adaptive Uncertainty Zones
- 在每个分裂节点引入可调宽度的不确定区域，用加权融合处理边界样本
- 五种估测方法均显著优于标准CART，margin法效率最高且无需调参
- 适用于需要可解释性与可信度评估的医疗等高风险场景
决策树对靠近和远离分裂阈值的样本赋予相同置信度。本文提出三元决策树，在每个分裂节点增加一个半宽为delta的不确定区域。通过决策论框架，将最优区域宽度delta*定义为局部成本最小化问题的解，并建立四条形式化性质：准确率分解、决定性准确率提升的充分条件、精确效率表征（eta = 决定准确率减去边界不确定预测准确率），以及边界法的渐近一致性。位于区域内的实例通过加权融合两个子树预测，并被标记为边界不确定。提出并评估五种delta估计方法：质量平台法（分裂准则曲线平台宽度）、类别重叠法（经验类别分布重叠）、增益比法（分裂质量相对于分裂熵）、节点自助法（节点重采样下的阈值方差）和边缘法（受SVM启发，到最近异类训练样本的距离）。所有方法复用标准CART分裂时已计算的统计量，无需外部噪声设定。在71/72个OpenML-CC18数据集上进行5折交叉验证，所有方法结合概率路由均显著优于标准CART的决定准确率（威尔科克森符号秩检验，p < 0.001）。边缘法实现最佳效率（每单位标记率带来0.104的准确率增益），在42/72个数据集上胜出，且无需超参数。在Breiman合成基准上的分析确认边缘法在干净数据上具备自校准能力。在乳腺钼靶数据上，节点自助法通过标记10.8%病例为边界不确定，实现+0.71%的决定准确率提升。
原文摘要 · Abstract (English)
Decision trees assign identical confidence to instances near and far from each split threshold. We introduce ternary decision trees, which augment each split node with an uncertainty zone of half-width delta. A decision-theoretic framework characterises the optimal zone width delta* as the solution to a node-local cost-minimisation problem; four formal properties are established: accuracy decomposition, a sufficiency condition for decided accuracy improvement, an exact efficiency characterisation (eta = Dec-Acc minus Acc_u, the accuracy gap between decided and boundary-uncertain predictions), and asymptotic consistency of the margin method. Instances within the zone receive predictions by weighted blending of both child subtrees and are flagged as boundary-uncertain. We propose and evaluate five delta-estimation methods: quality-plateau (plateau width of the split criterion curve), class-overlap (empirical class-distribution overlap), gain-ratio (split quality relative to split entropy), node-bootstrap (threshold variance under node-level resampling), and margin (SVM-inspired distance to the nearest cross-class training example). All methods reuse statistics already computed during standard CART split finding, requiring no external noise specification. Evaluated across 71 of the 72 OpenML-CC18 datasets with 5-fold cross-validation, all five methods with probabilistic routing significantly outperform standard CART on decided accuracy (Wilcoxon signed-rank, p < 0.001). The margin method achieves the best efficiency (0.104 accuracy gain per unit flagging rate), wins on 42 of 72 datasets, and requires zero hyperparameters. Analysis on Breiman synthetic benchmarks confirms margin is self-calibrating on clean data. On mammography, node-bootstrap achieves +0.71% decided accuracy by flagging 10.8% of cases as boundary-uncertain.
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