On the Computational Intelligibility of Boolean Classifiers

Abstract

In this paper, we investigate the computational intelligibility of Boolean classifiers, characterized by their ability to answer XAI queries in polynomial time. The classifiers under consideration are decision trees, DNF formulae, decision lists, decision rules, tree ensembles, and Boolean neural nets. Using 9 XAI queries, including both explanation queries and verification queries, we show the existence of large intelligibility gap between the families of classifiers. On the one hand, all the 9 XAI queries are tractable for decision trees. On the other hand, none of them is tractable for DNF formulae, decision lists, random forests, boosted decision trees, Boolean multilayer perceptrons, and binarized neural networks.

Efficient Explanations With Relevant Sets

“…κ : F → K. We now define formal explanations. Prime implicant (PI) explanations [36] denote a minimal set of literals (relating a feature value x i and a constant v i ∈ D i that are sufficient for the prediction 1 .…”

“…1 PI-explanations are related with abduction, and so are also referred to as abductive explanations (AXp) [14]. More recently, PI-explanations have been studied from a knowledge compilation perspective [2,1], but also in terms of their computational complexity [3].…”

“…Knowledge compilation (KC) languages [11] aim at simplifying queries and transformations in knowledge bases, and have recently been used as ML models. Concrete examples include binary decision diagrams [36,37], among others [2,3,1]. By noting that the explanation algorithm proposed for DTs exploits counting of models after conditioning (i.e.…”

“…Second, the paper shows that, in the case of DTs, a relaxed definition of δ-relevant set enables the computation of (relaxed) subset-minimal δ-relevant sets in polynomial time. Third, the paper shows that ML models based on knowledge compilation (KC) languages [11], including those studied in recent papers on XAI for KC languages [36,37,10,2,1], the computation of (relaxed) subset-minimal δ-relevant sets is also in polynomial time. Fourth, the paper shows that recently proposed duality results for explanations [15,13], which in practice enable the enumeration of explanations, can be extended to the setting of δ-relevant sets.…”

“…These approaches offer no formal guarantees of rigor, and practical limitations have been reported in recent years [8,28,38,19]. More recently, model-accurate non-heuristic approaches to explainability have been investigated [36,15,10,13,2,1,22]. These non-heuristic approaches are characterized by formal guarantees of rigor, e.g.…”