Explaining Multivariate Decision Trees: Characterising Tractable Languages

2026-05-29 · Source: Journal of Artificial Intelligence Research · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

This research investigates multivariate decision trees (MDTs), focusing on how the language of relations used to split feature space impacts their properties. A key aspect explored is the abductive explanation (AXp) for instance classification, defined as a minimal feature-value subset sufficient for the same decision. The study determines when finding a single AXp is tractable, identifying specific tractable languages for real, integer, and boolean features. For boolean languages, a P/NP-hard dichotomy is provided, which is extended to languages defined by formulas with literals corresponding to splits of ordered domains of arbitrary finite size. Experimental results suggest that MDTs offer more compact models than classical decision trees while preserving both accuracy and explainability.

Key takeaway

For AI scientists developing interpretable machine learning models, this research suggests considering multivariate decision trees (MDTs) as an alternative to classical decision trees. MDTs offer the potential for more compact models while maintaining accuracy and explainability. When designing systems that require abductive explanations (AXp), understanding the tractability conditions for different feature languages, particularly the P/NP-hard dichotomy for boolean and ordered domains, is crucial for efficient implementation and performance.

Key insights

Finding abductive explanations for multivariate decision trees is tractable for specific feature languages, offering compact, explainable models.

Principles

• MDTs can provide more compact models than classical decision trees.
• Tractability of abductive explanations depends on feature language.
• P/NP-hard dichotomy applies to boolean and ordered domains.

Topics

• Multivariate Decision Trees
• Abductive Explanations
• Computational Tractability
• P/NP-hard Dichotomy
• Model Explainability
• Feature Engineering

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Editorial summary, takeaway, and curation by AIssential. Original article published by Journal of Artificial Intelligence Research.