Causally Fair Node Classification on Non-IID Graph Data

TMLR Paper7064 Authors

Abstract: Fair machine learning seeks to identify and mitigate biases in predictions against unfavorable populations characterized by demographic attributes, such as race and gender. Recent research has extended fairness to graph data, such as social networks, but many neglect the causal relationships among data instances. This paper addresses the prevalent challenge in fair ML algorithms, which typically assume Independent and Identically Distributed (IID) data, from the causal perspective. Particularly, this work targets the circumstance where nodes with different neighborhood structures follow different causal mechanisms, violating the invariance assumptions required for classical structural causal models and $do$-calculus. We base our research on the Network Structural Causal Model (NSCM) framework and develop a Message Passing Variational Autoencoder for Causal Inference (MPVA) to compute interventional distributions for causally fair node classification. Theoretical soundness is established under two conditions: Decomposability and Graph Independence. These conditions formalize when causal mechanism heterogeneity can be overcome by constructing a structural representation that restores invariance and facilitates the computation of interventional distributions using $do$-calculus in non-IID settings. Empirical evaluations on semi-synthetic and real-world datasets demonstrate that MPVA outperforms conventional methods by effectively approximating interventional distributions and mitigating bias. The implications of our findings underscore the potential of causality-based fairness in complex ML applications, setting the stage for further research into relaxing the initial assumptions to enhance model fairness.

Submission Type: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

## Summary of Major Revisions

### 1. Theoretical Foundation and Clarity

We have substantially rewritten the theoretical sections (Section 5.1 and 5.2) to address concerns about rigor and clarity:

- **Clarified the fundamental challenge**: We now explicitly articulate that nodes with different neighborhood structures follow different causal mechanisms, violating the invariance assumptions required for classical structural causal models and $do$-calculus.

- **Enhanced theoretical exposition**: We added detailed explanations of how Decomposability and Graph Independence conditions enable the recovery of a shared causal mechanism despite neighborhood-dependent interactions. This includes explicit derivation of the reduced causal diagram and its structural equations.

- **New Proposition on Identifiability (Proposition 3)**: We added formal analysis to demonstrate when causal effects are identifiable under our conditions and when they fail (when Graph Independence is violated).

- **New Section 5.2 "From Identification to Estimation"**: We added this section to bridge theory and practice, explaining how the shared functional component $Q(x;\mathbf{s},c)$ can be learned from observational data and reused under intervention. This addresses the concern about the connection between theoretical results and the proposed method.

- **Revised Theorem 4 and Corollary 5**: We reformulated the main theoretical results with clearer statements and detailed intuition about the Monte Carlo interpretation for estimation.

### 2. Clarification of Method Contributions

We revised the abstract and introduction to:

- Clearly position our contribution as addressing causal mechanism heterogeneity in graph settings
- Explain that our method computes interventional distributions via the adjustment formula, addressing the confusion about identifiability
- Clarify how MPVA architecture is motivated by the theoretical decomposition

### 3. Experimental Design and Assumptions

We revised the experimental section:

- Added analysis of the accuracy-fairness trade-off
- Added sensitivity analysis when the assumptions are violated

Assigned Action Editor: ~Mingming_Gong1

Submission Number: 7064