Generating Robust Counterfactual Witnesses for Graph Neural Networks

This paper introduces a new class of explanation structures, called robust counterfactual witnesses (RCWs), to provide robust, both counterfactual and factual explanations for graph neural networks. Given a graph neural network M, a robust counterfactual witness refers to the fraction of a graph G that are counterfactual and factual explanation of the results of M over G, but also remains so for any "disturbed" G by flipping up to k of its node pairs. We establish the hardness results, from tractable results to co-NP-hardness, for verifying and generating robust counterfactual witnesses. We study such structures for GNN-based node classification, and present efficient algorithms to verify and generate RCWs. We also provide a parallel algorithm to verify and generate RCWs for large graphs with scalability guarantees. We experimentally verify our explanation generation process for benchmark datasets, and showcase their applications.

View-based Explanations for Graph Neural Networks

Generating explanations for graph neural networks (GNNs) has been studied to understand their behavior in analytical tasks such as graph classification. Existing approaches aim to understand the overall results of GNNs rather than providing explanations for specific class labels of interest, and may return explanation structures that are hard to access, nor directly queryable.We propose GVEX, a novel paradigm that generates Graph Views for EXplanation. (1) We design a two-tier explanation structure called explanation views. An explanation view consists of a set of graph patterns and a set of induced explanation subgraphs. Given a database G of multiple graphs and a specific class label l assigned by a GNN-based classifier M, it concisely describes the fraction of G that best explains why l is assigned by M. (2) We propose quality measures and formulate an optimization problem to compute optimal explanation views for GNN explanation. We show that the problem is $\Sigma^2_P$-hard. (3) We present two algorithms. The first one follows an explain-and-summarize strategy that first generates high-quality explanation subgraphs which best explain GNNs in terms of feature influence maximization, and then performs a summarization step to generate patterns. We show that this strategy provides an approximation ratio of 1/2. Our second algorithm performs a single-pass to an input node stream in batches to incrementally maintain explanation views, having an anytime quality guarantee of 1/4 approximation. Using real-world benchmark data, we experimentally demonstrate the effectiveness, efficiency, and scalability of GVEX. Through case studies, we showcase the practical applications of GVEX.