On Explaining Decision Trees

TL;DR

This paper challenges the common perception of decision trees as inherently interpretable by showing their paths can be arbitrarily large compared to minimal explanations, and introduces a polynomial-time method for computing these explanations.

Contribution

It proposes a novel polynomial-time algorithm for computing PI-explanations of decision trees and relates the enumeration of explanations to minimal hitting sets.

Findings

Decision tree paths often exceed minimal explanations in size.

The proposed method efficiently computes PI-explanations.

Experimental results confirm the discrepancy between paths and explanations.

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.