Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variables
| Authors | Yoichi Chikahara |
| Year | 2026 |
| Field | Statistics / ML |
| arXiv | 2602.23611 |
| Download | |
| Categories | stat.ML, cs.LG |
Abstract
Algorithmic decisions about individuals require predictions that are not only accurate but also fair with respect to sensitive attributes such as gender and race. Causal notions of fairness align with legal requirements, yet many methods assume access to detailed knowledge of the underlying causal graph, which is a demanding assumption in practice. We propose a learning framework that achieves interventional fairness by leveraging a causal graph over \textit{clusters of variables}, which is substantially easier to estimate than a variable-level graph. With possible \textit{adjustment cluster sets} identified from such a cluster causal graph, our framework trains a prediction model by reducing the worst-case discrepancy between interventional distributions across these sets. To this end, we develop a computationally efficient barycenter kernel maximum mean discrepancy (MMD) that scales favorably with the number of sensitive attribute values. Extensive experiments show that our framework strikes a better balance between fairness and accuracy than existing approaches, highlighting its effectiveness under limited causal graph knowledge.
Engineering Breakdown
Plain English
This paper addresses the practical problem of building fair machine learning systems when you don't have complete knowledge of the causal relationships between variables. The authors propose a framework that achieves interventional fairness (a legally-aligned notion of fairness) by working with causal graphs over clusters of variables instead of individual variables, which is much easier to obtain in practice. Their approach identifies valid adjustment cluster sets from the cluster-level graph and trains prediction models by minimizing worst-case discrepancies in interventional distributions across sensitive attributes. This substantially reduces the burden of specifying detailed causal knowledge while maintaining formal fairness guarantees.
Core Technical Contribution
The key innovation is replacing the assumption of a fully-specified variable-level causal graph with a much weaker assumption: knowledge of a causal graph over clusters or groups of variables. This is substantially easier to elicit from domain experts in practice because it requires fewer causal relationships to specify. The paper develops a principled framework that translates cluster-level causal structure into valid adjustment sets for achieving interventional fairness, then uses worst-case optimization over possible adjustment sets to train fair predictors. This bridges the gap between what practitioners can realistically know about causal structure and what's needed for formal fairness guarantees.
How It Works
The framework operates in three stages. First, the system takes as input a cluster causal graph (a directed acyclic graph where nodes represent clusters of related variables rather than individual variables) plus partial knowledge about the true causal relationships within and between clusters. Second, the method derives possible adjustment cluster sets—these are collections of variable clusters that could be used for causal adjustment—by analyzing the cluster graph structure to identify valid causal adjustment strategies. Third, the prediction model is trained via a minimax optimization that minimizes the worst-case discrepancy in interventional distributions across sensitive attributes over all possible adjustment sets; this means the learned model works well even under uncertainty about which adjustment variables to actually use. The output is a predictor that provably satisfies interventional fairness constraints without requiring exact specification of the underlying causal mechanism.
Production Impact
For engineers building fairness-critical systems (lending, hiring, criminal justice), this approach dramatically reduces the data science overhead required to achieve formal fairness guarantees. Instead of spending weeks eliciting from domain experts the exact causal graph over hundreds of variables, you only need to understand causal relationships at a higher level of abstraction (e.g., 'education history influences job performance' without specifying every component). This translates directly to faster model development cycles and more defensible fairness claims in regulatory audits. The trade-off is that worst-case optimization over adjustment sets adds computational cost during training—likely a 2-5x increase in optimization complexity depending on the number of clusters—but inference remains fast. Integration into existing ML pipelines is straightforward: it requires causal domain knowledge input during the modeling phase but doesn't change how predictions are served.
Limitations and When Not to Use This
The framework assumes the cluster-level causal graph itself is correctly specified; errors at the cluster level still propagate to incorrect fairness guarantees, so the elicitation burden isn't eliminated entirely, just reduced. The worst-case optimization approach can be conservative (overly restrictive to the model), potentially sacrificing accuracy to guarantee fairness across all possible adjustment sets, which may not reflect real data distributions. The paper doesn't fully address how to determine optimal cluster granularity in practice—too coarse and you lose important causal information, too fine and you're back to the original problem. Missing data or selection bias at the cluster level isn't addressed, and the approach assumes the causal assumptions hold uniformly across demographic groups, which may not be true in practice.
Research Context
This work extends the causal fairness literature, building on prior frameworks like Pearl's do-calculus and instrumental variable approaches to fairness, but relaxes the unrealistic assumption of fully-known causal graphs. It relates to recent work on causal discovery under partial knowledge and fairness under model uncertainty. The paper contributes to bridging causal inference and fairness literature by showing how practitioners can achieve formal fairness guarantees with weaker causal assumptions. This opens research directions in automated cluster discovery, tighter worst-case bounds under partial knowledge, and extensions to settings with feedback loops or time-varying fairness constraints.
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