aiqbench analysis
This research introduces ternary decision trees that incorporate locally-adaptive uncertainty zones to address the standard CART limitation of assigning uniform confidence near split thresholds. By leveraging decision-theoretic optimization and reusing existing split statistics, the proposed methods achieve significant accuracy improvements while explicitly flagging boundary-uncertain instances without requiring external noise specifications. The study demonstrates that the margin-based estimation method offers the best efficiency with zero hyperparameters, validating the approach across a comprehensive dataset of 71 benchmarks.
Ternary Decision Trees with Locally-Adaptive Uncertainty Zones
arXiv:2605.22740v2 Announce Type: replace Abstract: 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.
Abstract: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.
V2: Major revision. Added decision-theoretic framework deriving optimal delta* as a node-local cost minimisation problem; four formal theoretical properties (Propositions 1-4); motivating example figure (Figure 5); strengthened related work and limitations analysis. 15 pages, 5 figures, 5 appendix sections. Submitted to Data Mining and Knowledge Discovery (DAMI)
Machine Learning (cs.LG)
arXiv:2605.22740 [cs.LG]
(or arXiv:2605.22740v2 [cs.LG] for this version)
Full text under the publisher's open licence · 299 words