[Paper Review] On Explaining Decision Trees

Yacine Izza, Alexey Ignatiev+1 more|arXiv (Cornell University)|Oct 21, 2020

Explainable Artificial Intelligence (XAI)70 references44 citations

TL;DR

The paper shows that decision trees can be less interpretable than PI-explanations (subset-minimal feature-value sets) and provides a polynomial-time method to compute a single PI-explanation, plus a hitting-set approach to enumerate PI-explanations for DTs; experiments reveal many DT paths are explanation-redundant.

ABSTRACT

Decision trees (DTs) epitomize what have become to be known as interpretable machine learning (ML) models. This is informally motivated by paths in DTs being often much smaller than the total number of features. This paper shows that in some settings DTs can hardly be deemed interpretable, with paths in a DT being arbitrarily larger than a PI-explanation, i.e. a subset-minimal set of feature values that entails the prediction. As a result, the paper proposes a novel model for computing PI-explanations of DTs, which enables computing one PI-explanation in polynomial time. Moreover, it is shown that enumeration of PI-explanations can be reduced to the enumeration of minimal hitting sets. Experimental results were obtained on a wide range of publicly available datasets with well-known DT-learning tools, and confirm that in most cases DTs have paths that are proper supersets of PI-explanations.

Motivation & Objective

• Demonstrate that some decision trees contain explanation-redundant paths that are larger than minimal PI-explanations.
• Introduce a polynomial-time method to compute a single PI-explanation for a given instance in a DT.
• Formulate PI-explanation enumeration for DTs via minimal hitting sets (MHSes).
• Provide empirical evidence on standard DT-learning tools that DT paths often extend beyond minimal explanations.

Proposed method

• Define PI-explanations as subset-minimal literals implying the prediction.
• Propose a polynomial-time algorithm to compute one PI-explanation for a given instance in a DT.
• Reduce PI-explanation enumeration to enumerating minimal hitting sets and solve via iterative NP-oracle calls (e.g., SAT/ILP).
• Develop a linear-time algorithm to decide explanation-redundancy for DT paths by checking if a literal can be dropped while preserving the prediction.
• Differentiate path-restricted versus path-unrestricted PI-explanations.
• Present algorithms (Algorithm 1 and Algorithm 2) for redundancy analysis and (for PI-explanations) Algorithm 3-like approach for enumeration via subsets hitting sets.

Experimental results

Research questions

• RQ1 Do decision tree paths provide explanations that are redundant relative to minimal PI-explanations?
• RQ2 Can we compute a single PI-explanation for a DT efficiently (polynomial time) and enumerate all PI-explanations via hitting sets?
• RQ3 How often do DT paths include more literals than necessary to entail a prediction across public datasets?
• RQ4 What is the impact of path-restricted versus path-unrestricted PI-explanations in practice?

Key findings

• There exist Boolean functions where irreducible DTs contain paths that are proper supersets of PI-explanations, with the difference growing with the number of features.
• Empirical results show many learned DTs have explanation-redundant paths; often, a constant-size PI-explanation suffices for a given prediction.
• A polynomial-time algorithm can compute a single PI-explanation from a given DT path.
• Enumeration of PI-explanations can be reduced to enumerating minimal hitting sets; the authors propose a solution based on iterative NP oracle calls.
• Experimentally, explanation-redundancy is prevalent across datasets and DT-learning tools (IAI and ITI) with reasonable runtime for extracting PI-explanations.