Counterfactual Explanations for Graph Classification Through the Lenses of Density

TL;DR

This paper introduces a density-based framework for generating counterfactual explanations in graph classification, focusing on dense substructures like triangles and cliques to produce more meaningful and interpretable explanations.

Contribution

The authors propose a novel density-based counterfactual search framework for graph classifiers, with specific methods for triangles and cliques, enhancing interpretability over traditional edge manipulation.

Findings

Effective in 7 brain network datasets

Density-based explanations are more interpretable

Outperforms edge-based counterfactual methods

Abstract

Counterfactual examples have emerged as an effective approach to produce simple and understandable post-hoc explanations. In the context of graph classification, previous work has focused on generating counterfactual explanations by manipulating the most elementary units of a graph, i.e., removing an existing edge, or adding a non-existing one. In this paper, we claim that such language of explanation might be too fine-grained, and turn our attention to some of the main characterizing features of real-world complex networks, such as the tendency to close triangles, the existence of recurring motifs, and the organization into dense modules. We thus define a general density-based counterfactual search framework to generate instance-level counterfactual explanations for graph classifiers, which can be instantiated with different notions of dense substructures. In particular, we show two specific instantiations of this general framework: a method that searches for counterfactual graphs by opening or closing triangles, and a method driven by maximal cliques. We also discuss how the general method can be instantiated to exploit any other notion of dense substructures, including, for instance, a given taxonomy of nodes. We evaluate the effectiveness of our approaches in 7 brain network datasets and compare the counterfactual statements generated according to several widely-used metrics. Results confirm that adopting a semantic-relevant unit of change like density is essential to define versatile and interpretable counterfactual explanation methods.