Evidence-typed split criteria for decision trees under label noise: what one and two label sources can support
DOI:
https://doi.org/10.5281/zenodo.22712876Keywords:
decision trees, split criteria, label noise, annotated logic, multiple annotators, educational data miningAbstract
Annotated and neutrosophic logics assign separate degrees of favourable and contrary evidence, which suggests split criteria for decision trees that take contradictory nodes into account. We examine what such criteria can support under label noise. The index 2TF + λ·min(T, F) equals Gini plus λ times the resubstitution error; it reverses Gini's ranking of splits on nodes of 10 instances, and a margin condition states when a Gini split survives. Contradiction in the sense of these logics needs independent evidence: with one label source the annotated-logic degree of contradiction vanishes, while with two sources the paired share of instances whose labels disagree measures it instance by instance. On seven independent binary datasets with 50 resampled folds and injected label noise, λ = 0.35 changed the root split in up to 24% of folds, and none of 3222 root flips violated the margin. At depth 4 an exploratory random-effects analysis added after review showed accuracy equivalent to Gini within ±1 percentage point at noise levels up to 25%, although the prespecified cell-by-cell equivalence was not established. In depth-8 trees under heavy noise the penalised criteria gained accuracy and grew smaller trees, as did misclassification error and cost-complexity pruning. With two noisy labels, using the contradiction status of each instance to exclude contradicted instances from the consensus label score gained 1.73 points in deep trees under instance-dependent noise and averaging the labels helped, whereas adding contradiction as an impurity penalty brought no detectable benefit.
Received: 3 August 2026 | Accepted: 12 September 2026
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