Graph-structured data is ubiquitous and powerful in representing complex relationships in many online platforms. While graph neural networks (GNNs) are widely used to learn from such data, counterfactual graph learning has emerged as a promising approach to improve model interpretability. Counterfactual explanation research focuses on identifying a counterfactual graph that is similar to the original but leads to different predictions. These explanations optimize two objectives simultaneously: the sparsity of changes in the counterfactual graph and the validity of its predictions. Building on these qualitative optimization goals, this paper introduces CFRecs, a novel framework that transforms counterfactual explanations into actionable insights. CFRecs employs a two-stage architecture consisting of a graph neural network (GNN) and a graph variational auto-encoder (Graph-VAE) to strategically propose minimal yet high-impact changes in graph structure and node attributes to drive desirable outcomes in recommender systems. We apply CFRecs to Zillow's graph-structured data to deliver actionable recommendations for both home buyers and sellers with the goal of helping them navigate the competitive housing market and achieve their homeownership goals. Experimental results on Zillow's user-listing interaction data demonstrate the effectiveness of CFRecs, which also provides a fresh perspective on recommendations using counterfactual reasoning in graphs.

Probabilities of causation provide principled ways to assess causal relationships but face computational challenges due to partial identifiability and latent confounding. This paper introduces both algorithmic simplifications, significantly reducing the computational complexity of calculating tighter bounds for these probabilities, and a novel methodological framework for Root Cause Analysis that systematically employs these causal metrics to rank entire causal paths.

Graph Neural Networks (GNNs) have been widely deployed in various real-world applications. However, most GNNs are black-box models that lack explanations. One strategy to explain GNNs is through counterfactual explanation, which aims to find minimum perturbations on input graphs that change the GNN predictions. Existing works on GNN counterfactual explanations primarily concentrate on the local-level perspective (i.e., generating counterfactuals for each individual graph), which suffers from information overload and lacks insights into the broader cross-graph relationships. To address such issues, we propose GlobalGCE, a novel global-level graph counterfactual explanation method. GlobalGCE aims to identify a collection of subgraph mapping rules as counterfactual explanations for the target GNN. According to these rules, substituting certain significant subgraphs with their counterfactual subgraphs will change the GNN prediction to the desired class for most graphs (i.e., maximum coverage). Methodologically, we design a significant subgraph generator and a counterfactual subgraph autoencoder in our GlobalGCE, where the subgraphs and the rules can be effectively generated. Extensive experiments demonstrate the superiority of our GlobalGCE compared to existing baselines. Our code can be found at https://anonymous.4open.science/r/GlobalGCE-92E8.

Explainable Artificial Intelligence (XAI) has emerged as a critical area of research to unravel the opaque inner logic of (deep) machine learning models. Among the various XAI techniques proposed in the literature, counterfactual explanations stand out as one of the most promising approaches. However, these ``what-if'' explanations are frequently complex and technical, making them difficult for non-experts to understand and, more broadly, challenging for humans to interpret. To bridge this gap, in this work, we exploit the power of open-source Large Language Models to generate natural language explanations when prompted with valid counterfactual instances produced by state-of-the-art explainers for graph-based models. Experiments across several graph datasets and counterfactual explainers show that our approach effectively produces accurate natural language representations of counterfactual instances, as demonstrated by key performance metrics.

Causal structure discovery methods are commonly applied to structured data where the causal variables are known and where statistical testing can be used to assess the causal relationships. By contrast, recovering a causal structure from unstructured natural language data such as news articles contains numerous challenges due to the absence of known variables or counterfactual data to estimate the causal links. Large Language Models (LLMs) have shown promising results in this direction but also exhibit limitations. This work investigates LLM's abilities to build causal graphs from text documents and perform counterfactual causal inference. We propose an end-to-end causal structure discovery and causal inference method from natural language: we first use an LLM to extract the instantiated causal variables from text data and build a causal graph. We merge causal graphs from multiple data sources to represent the most exhaustive set of causes possible. We then conduct counterfactual inference on the estimated graph. The causal graph conditioning allows reduction of LLM biases and better represents the causal estimands. We use our method to show that the limitations of LLMs in counterfactual causal reasoning come from prediction errors and propose directions to mitigate them. We demonstrate the applicability of our method on real-world news articles.

Graph-level anomaly detection is significant in diverse domains. To improve detection performance, counterfactual graphs have been exploited to benefit the generalization capacity by learning causal relations. Most existing studies directly introduce perturbations (e.g., flipping edges) to generate counterfactual graphs, which are prone to alter the semantics of generated examples and make them off the data manifold, resulting in sub-optimal performance. To address these issues, we propose a novel approach, Motif-consistent Counterfactuals with Adversarial Refinement (MotifCAR), for graph-level anomaly detection. The model combines the motif of one graph, the core subgraph containing the identification (category) information, and the contextual subgraph (non-motif) of another graph to produce a raw counterfactual graph. However, the produced raw graph might be distorted and cannot satisfy the important counterfactual properties: Realism, Validity, Proximity and Sparsity. Towards that, we present a Generative Adversarial Network (GAN)-based graph optimizer to refine the raw counterfactual graphs. It adopts the discriminator to guide the generator to generate graphs close to realistic data, i.e., meet the property Realism. Further, we design the motif consistency to force the motif of the generated graphs to be consistent with the realistic graphs, meeting the property Validity. Also, we devise the contextual loss and connection loss to control the contextual subgraph and the newly added links to meet the properties Proximity and Sparsity. As a result, the model can generate high-quality counterfactual graphs. Experiments demonstrate the superiority of MotifCAR.

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.

Graph neural networks (GNNs) find applications in various domains such as computational biology, natural language processing, and computer security. Owing to their popularity, there is an increasing need to explain GNN predictions since GNNs are black-box machine learning models. One way to address this is counterfactual reasoning where the objective is to change the GNN prediction by minimal changes in the input graph. Existing methods for counterfactual explanation of GNNs are limited to instance-specific local reasoning. This approach has two major limitations of not being able to offer global recourse policies and overloading human cognitive ability with too much information. In this work, we study the global explainability of GNNs through global counterfactual reasoning. Specifically, we want to find a small set of representative counterfactual graphs that explains all input graphs. Towards this goal, we propose GCFExplainer, a novel algorithm powered by vertex-reinforced random walks on an edit map of graphs with a greedy summary. Extensive experiments on real graph datasets show that the global explanation from GCFExplainer provides important high-level insights of the model behavior and achieves a 46.9% gain in recourse coverage and a 9.5% reduction in recourse cost compared to the state-of-the-art local counterfactual explainers.

Counterfactual statements, e.g., "my headache would be gone had I taken an aspirin" are central to scientific discourse, and are formally interpreted as statements derived from "alternative worlds". However, since they invoke hypothetical states of affairs, often incompatible with what is actually known or observed, testing counterfactuals is fraught with conceptual and practical difficulties. In this paper, we provide a complete characterization of "testable counterfactuals," namely, counterfactual statements whose probabilities can be inferred from physical experiments. We provide complete procedures for discerning whether a given counterfactual is testable and, if so, expressing its probability in terms of experimental data.

Many applications of causal analysis call for assessing, retrospectively, the effect of withholding an action that has in fact been implemented. This counterfactual quantity, sometimes called "effect of treatment on the treated," (ETT) have been used to to evaluate educational programs, critic public policies, and justify individual decision making. In this paper we explore the conditions under which ETT can be estimated from (i.e., identified in) experimental and/or observational studies. We show that, when the action invokes a singleton variable, the conditions for ETT identification have simple characterizations in terms of causal diagrams. We further give a graphical characterization of the conditions under which the effects of multiple treatments on the treated can be identified, as well as ways in which the ETT estimand can be constructed from both interventional and observational distributions.