Relevance-Aware Rule: Structural Deletion of Irrelevant Conditions in Decision Trees

Decision trees generate interpretable if--then rules, yet they contain irrelevant conditions (IRCs). These IRCs arise from the structural mechanism of tree splitting and persist even in modern optimal sparse tree induction algorithms. Existing IRC deletion methods overlook this structural mechanism; therefore, they either preserve the original tree too loosely to remain reliable, or too strictly to achieve meaningful simplification. This study provides theoretical foundations for reliable IRC deletion by establishing theorems and propositions related to the underlying IRC mechanism. The key finding is that a binary split shifts class proportions in opposite directions relative to the parent. Specifically, an increase in the class-1 proportion along one branch necessitates an increase in the class-0 proportion along its sibling, thereby generating a C1-link and a C0-link. Based on this structural fact, we propose a structural IRC deletion framework. Relative to each leaf, links that increase the leaf-class proportion are matched, whereas links that increase the proportion of the opposite leaf-class are mismatched. These mismatched links are flagged as structurally suspicious IRC candidates. Rather than deleting them outright, the framework rigorously diagnoses their relevance by assessing prediction reliability. It selectively deletes conditions that are structurally and empirically irrelevant, while strictly protecting those whose deletion would reduce the rule's reliability. Experimental results confirm that the proposed framework achieves substantial rule simplification without sacrificing the reliability of the original tree.