CIDER: Counterfactual-Invariant Diffusion-based GNN Explainer for Causal Subgraph Inference

Abstract: Inferring causal links or subgraphs corresponding to a specific phenotype or label based solely on measured data is an important yet challenging task, which is also different from inferring causal nodes. While Graph Neural Network (GNN) Explainers have shown potential in subgraph identification, existing methods with GNN often offer associative rather than causal insights. This lack of transparency and explainability hinders our understanding of their results and also underlying mechanisms. To address this issue, we propose a novel method of causal link/subgraph inference, called CIDER: Counterfactual-Invariant Diffusion-based GNN ExplaineR, by implementing both counterfactual and diffusion implementations. In other words, it is a model-agnostic and task-agnostic framework for generating causal explanations based on a counterfactual-invariant and diffusion process, which provides not only causal subgraphs due to counterfactual implementation but reliable causal links due to the diffusion process. Specifically, CIDER is first formulated as an inference task that generatively provides the two distributions of one causal subgraph and another spurious subgraph. Then, to enhance the reliability, we further model the CIDER framework as a diffusion process. Thus, using the causal subgraph distribution, we can explicitly quantify the contribution of each subgraph to a phenotype/label in a counterfactual manner, representing each subgraph's causal strength. From a causality perspective, CIDER is an interventional causal method, different from traditional association studies or observational causal approaches, and can also reduce the effects of unobserved confounders. We evaluate CIDER on both synthetic and real-world datasets, which all demonstrate the superiority of CIDER over state-of-the-art methods.

• The paper introduces CIDER, a novel framework employing counterfactual-invariant diffusion to infer causal subgraphs for explaining Graph Neural Network predictions.
• CIDER leverages variational inference to differentiate causal from spurious subgraphs through counterfactual diversity and refines results via a robust diffusion process.
• Empirical evaluation shows CIDER surpasses existing methods on datasets like MUTAG and NCI1 and demonstrates practical utility in analyzing complex biological data.

An Overview of the CIDER Framework for Causal Subgraph Inference

Graph Neural Networks (GNNs) have become fundamental tools for processing and interpreting graph-structured data prevalent in numerous domains, including bioinformatics and social network analysis. Despite the potential of GNNs in identifying subgraphs relevant to specific outputs, current methods often lack causal clarity and are limited to associative insights. The paper "CIDER: Counterfactual-Invariant Diffusion-based GNN Explainer for Causal Subgraph Inference" proposes a novel framework aimed at overcoming these limitations by providing causal explanations via a counterfactual-invariant diffusion process.

The CIDER Approach

CIDER (Counterfactual-Invariant Diffusion-based GNN ExplaineR) addresses the challenge of extracting causal subgraphs from given graph data. It offers a model-agnostic and task-agnostic method to furnish causal explanations by integrating counterfactual reasoning with a diffusion mechanism.

1. Counterfactual-Invariant Process: CIDER emphasizes counterfactual reasoning, which determines subgraphs causally linked to specific phenotypes or labels. By leveraging variational inference to generate subgraph distributions, this process helps distinguish causal from spurious subgraphs. The counterfactual diversity is formulated by estimating the marginal distribution of spurious subgraphs conditioned on causal subgraphs.
2. Diffusion Mechanism: The method incorporates a diffusion-based inference framework, modeling the initial network as distributionally equivalent to the causal subgraph infused with noisy spurious subgraphs. Over a series of diffusion steps, CIDER refines and targets the subgraph with causal edges, promising robustness against noise and unobserved confounders.
3. Optimization Framework: The optimization involves minimizing the reconstruction error along with Kullback-Leibler divergence, capturing the causal subgraph distribution while considering the variational distribution of spurious subgraphs.

Empirical Evaluation

The authors evaluate CIDER's efficacy on both synthetic and real-world datasets, including datasets like BA-2motif, MUTAG, and NCI1, which are commonly used for graph classification tasks.

• On the BA-2motif dataset, CIDER nearly achieves 100% accuracy in distinguishing motif types, showcasing its proficiency in handling synthetic data where ground truth is known.
• For real-world datasets MUTAG and NCI1, CIDER consistently surpasses existing methods, demonstrating its applicability in complex, authentic scenarios.

Additionally, CIDER is applied to biological data, such as single-cell RNA-seq data related to COVID-19 and RNA-seq data of acute myeloid leukemia from TCGA-LAML. These applications reveal CIDER's practicality in biological insight discovery, identifying key genes and cell types implicated in disease mechanisms.

Theoretical Contributions

CIDER's distinctiveness is underpinned by its theoretical foundation in causal inference. In contrast to association-based studies or observational approaches, CIDER reduces the impact of confounders through interventional causality. Hence, it has the potential to deduce more accurate representations of phenomena across diverse domains, such as identifying diseases' molecular mechanisms or clarifying network interactions in social platforms.

Future Directions

In fostering the development of causal inference models, CIDER opens pathways for advancing research in both theoretical and applied domains. Potential future work could explore the expansion of CIDER into hypergraph scenarios or further validate unobserved confounder handling in real-world settings. Additionally, incorporating this framework into broader AI systems could enhance explainability and trustworthiness, pivotal for both scientific inquiries and societal applications.

In sum, the paper presents CIDER as a robust method offering causal insights into GNN-model outputs, with implications spanning diverse applications where discerning causal relationships is paramount.