arXiv:2509.17774cs.AIcs.LG2025-09被引 1

提出高效正确判定决策树预测等价的新方法,解决原有算法慢且出错问题。

Efficient & Correct Predictive Equivalence for Decision Trees

  • 基于多项式时间算法替代原复杂度的Quine-McCluskey法
  • 证明原方法在特定树结构下会指数级耗时且可能误判等价性
  • 适用于需要准确特征重要性或缺失数据推理的场景

决策树的Rashomon集包含大量预测等价的树,这些冗余会导致特征重要性计算失准。现有方法依赖Quine-McCluskey(QM)求最小项析取范式(DNF)以判断等价性,但该方法属于多项式层次第二层难题,最坏情况需指数时间与空间。本文首次证明存在触发其指数开销的决策树;其次指出若未满足两个关键约束,QM可能错误判断等价性,且难以形式化保证;最后证明所有依赖最小DNF的问题均可在决策树规模的多项式时间内解决。实验表明,对于易受旧法影响的树,新算法提速达数量级。

原文摘要 · Abstract (English)

The Rashomon set of decision trees (DTs) finds importance uses. Recent work showed that DTs computing the same classification function, i.e. predictive equivalent DTs, can represent a significant fraction of the Rashomon set. Such redundancy is undesirable. For example, feature importance based on the Rashomon set becomes inaccurate due the existence of predictive equivalent DTs, i.e. DTs with the same prediction for every possible input. In recent work, McTavish et al. proposed solutions for several computational problems related with DTs, including that of deciding predictive equivalent DTs. The approach of McTavish et al. consists of applying the well-known method of Quine-McCluskey (QM) for obtaining minimum-size DNF (disjunctive normal form) representations of DTs, which are then used for comparing DTs for predictive equivalence. Furthermore, the minimum-size DNF representation was also applied to computing explanations for the predictions made by DTs, and to finding predictions in the presence of missing data. However, the problem of formula minimization is hard for the second level of the polynomial hierarchy, and the QM method may exhibit worst-case exponential running time and space. This paper first demonstrates that there exist decision trees that trigger the worst-case exponential running time and space of the QM method. Second, the paper shows that the QM method may incorrectly decide predictive equivalence, if two key constraints are not respected, and one may be difficult to formally guarantee. Third, the paper shows that any of the problems to which the smallest DNF representation has been applied to can be solved in polynomial time, in the size of the DT. The experiments confirm that, for DTs for which the worst-case of the QM method is triggered, the algorithms proposed in this paper are orders of magnitude faster than the ones proposed by McTavish et al.

决策树等价判定算法优化

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