On the Complexity of Global Necessary Reasons to Explain Classification

TL;DR

This paper analyzes the computational complexity of identifying minimal necessary reasons for classifier decisions in explainable AI, focusing on global explanations and their inherent computational challenges.

Contribution

It provides a thorough complexity analysis of the problem of finding minimal necessary conditions for classifier decisions across various classifier families.

Findings

Complexity results vary depending on classifier type.

Identifies classes of classifiers where the problem is computationally hard.

Provides insights into the feasibility of generating global explanations.

Abstract

Explainable AI has garnered considerable attention in recent years, as understanding the reasons behind decisions or predictions made by AI systems is crucial for their successful adoption. Explaining classifiers' behavior is one prominent problem. Work in this area has proposed notions of both local and global explanations, where the former are concerned with explaining a classifier's behavior for a specific instance, while the latter are concerned with explaining the overall classifier's behavior regardless of any specific instance. In this paper, we focus on global explanations, and explain classification in terms of ``minimal'' necessary conditions for the classifier to assign a specific class to a generic instance. We carry out a thorough complexity analysis of the problem for natural minimality criteria and important families of classifiers considered in the literature.