Explaining Multivariate Decision Trees: Characterising Tractable Languages

Abstract

We study multivariate decision trees (MDTs), in particular, classes of MDTs determined by the language of relations that can be used to split feature space. An abductive explanation (AXp) of the classification of a particular instance, viewed as a set of feature-value assignments, is a minimal subset of the instance which is sufficient to lead to the same decision. We investigate when finding a single AXp is tractable. We identify tractable languages for real, integer and boolean features. Indeed, in the case of boolean languages, we provide a P/NP-hard dichotomy. We extend this dichotomy to languages defined by formulas whose literals correspond to splits of ordered domains of arbitrary finite size. Experiments indicate that MDTs can provide more compact models than classical decision trees while conserving accuracy and explainability.