Efficient & Correct Predictive Equivalence for Decision Trees

2025-09-22

AI Summary

Inefficient and erroneous prediction equivalence checking in decision trees leads to redundant Rashomon sets, undermining the accuracy of feature importance analysis. Existing Quine-McCluskey (QM)-based approaches for computing minimal disjunctive normal forms suffer from worst-case exponential time and space complexity and may incorrectly assess equivalence. This paper identifies fundamental theoretical limitations of QM-based methods and proposes the first polynomial-time algorithm for prediction equivalence verification. Instead of relying on Boolean formula minimization, our approach performs logical simplification and structured equivalence checking directly on the original decision tree structure. We formally prove its correctness and polynomial-time solvability. Empirical evaluation demonstrates speedups of several orders of magnitude over QM on its worst-case instances, while guaranteeing exact, provably correct equivalence judgments.

Technology Category

• Machine Learning: Ensemble Methods
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

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. This approach, which this paper refers to as MBDSR, 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 MBDSR approach can produce incorrect results for the problem of deciding predictive equivalence. Third, the paper shows that any of the problems to which the minimum-size DNF representation has been applied to can in fact be solved in polynomial time, in the size of the DT. The experiments confirm that, for DTs for which the 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.

Problem

• Detecting predictive equivalence among decision trees efficiently
• Addressing exponential complexity of Quine-McCluskey method for DTs
• Correcting inaccurate predictive equivalence results from MBDSR approach

Innovation

• Identifies exponential complexity in Quine-McCluskey method
• Demonstrates incorrect equivalence results from MBDSR approach
• Proposes polynomial-time algorithms for decision tree problems