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Formally Explaining Decision Tree Models with Answer Set Programming

Akihiro Takemura, Masayuki Otani, Katsumi Inoue

TL;DR

This work tackles the challenge of providing formal, verifiable explanations for decision tree models and their ensembles. It introduces ASP encodings to generate four explanation types—sufficient, contrastive, majority, and tree-specific—for decision trees, random forests, and boosted trees, with the ability to enumerate multiple explanations under user constraints. Empirical results on 20 datasets show the ASP approach can match or surpass SAT-based methods for several explanation types, while also revealing scalability bottlenecks in large forests. The framework offers a flexible, unified, logic-based tool for explainable AI that can incorporate domain-specific constraints and preferences.

Abstract

Decision tree models, including random forests and gradient-boosted decision trees, are widely used in machine learning due to their high predictive performance. However, their complex structures often make them difficult to interpret, especially in safety-critical applications where model decisions require formal justification. Recent work has demonstrated that logical and abductive explanations can be derived through automated reasoning techniques. In this paper, we propose a method for generating various types of explanations, namely, sufficient, contrastive, majority, and tree-specific explanations, using Answer Set Programming (ASP). Compared to SAT-based approaches, our ASP-based method offers greater flexibility in encoding user preferences and supports enumeration of all possible explanations. We empirically evaluate the approach on a diverse set of datasets and demonstrate its effectiveness and limitations compared to existing methods.

Formally Explaining Decision Tree Models with Answer Set Programming

TL;DR

This work tackles the challenge of providing formal, verifiable explanations for decision tree models and their ensembles. It introduces ASP encodings to generate four explanation types—sufficient, contrastive, majority, and tree-specific—for decision trees, random forests, and boosted trees, with the ability to enumerate multiple explanations under user constraints. Empirical results on 20 datasets show the ASP approach can match or surpass SAT-based methods for several explanation types, while also revealing scalability bottlenecks in large forests. The framework offers a flexible, unified, logic-based tool for explainable AI that can incorporate domain-specific constraints and preferences.

Abstract

Decision tree models, including random forests and gradient-boosted decision trees, are widely used in machine learning due to their high predictive performance. However, their complex structures often make them difficult to interpret, especially in safety-critical applications where model decisions require formal justification. Recent work has demonstrated that logical and abductive explanations can be derived through automated reasoning techniques. In this paper, we propose a method for generating various types of explanations, namely, sufficient, contrastive, majority, and tree-specific explanations, using Answer Set Programming (ASP). Compared to SAT-based approaches, our ASP-based method offers greater flexibility in encoding user preferences and supports enumeration of all possible explanations. We empirically evaluate the approach on a diverse set of datasets and demonstrate its effectiveness and limitations compared to existing methods.
Paper Structure (27 sections, 3 equations, 4 figures, 6 tables)

This paper contains 27 sections, 3 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Boolean Functions
  4. Trees and Forests
  5. Decision Trees.
  6. Random Forests.
  7. Regression Trees and Forests.
  8. Boosted Trees.
  9. Answer Set Programming
  10. Explaining Decision Tree Models
  11. Decision Tree
  12. Sufficient Explanation from a Decision Tree
  13. Contrastive Explanation from a Decision Tree
  14. Worked Example: Sufficient Explanations from a Decision Tree
  15. Random Forest
  16. ...and 12 more sections

Figures (4)

  • Figure 1: Example decision tree for Boolean attributes.
  • Figure 2: A decision tree with three internal nodes.
  • Figure 3: A random forest with three trees.
  • Figure 4: Boosted tree model with three regression trees.

Theorems & Definitions (13)

  • Definition 1: Sufficient Explanation audemardExplanatoryPowerBoolean2022
  • Definition 2: Contrastive Explanation audemardExplanatoryPowerBoolean2022
  • Definition 3: Sufficient Explanation audemardTradingComplexitySparsity2022
  • Definition 4: Contrastive Explanation audemardTradingComplexitySparsity2022
  • Definition 5: Majority Explanation audemardTradingComplexitySparsity2022
  • Definition 6: Best and Worst Instance audemardComputingAbductiveExplanations2023b
  • Definition 7: Tree-Specific Explanation audemardComputingAbductiveExplanations2023b
  • Example 1: Sufficient Explanation
  • Example 2: Contrastive Explanation
  • Example 3: Sufficient Explanation
  • ...and 3 more