Causal Graph Counterfactual Debiasing

• Causal graph-based counterfactual debiasing is a method that uses causal graphs and counterfactual interventions to diagnose and mitigate both direct and indirect bias in predictions.
• It employs data augmentation, invariance enforcement, and stable feature selection to ensure model outputs remain unbiased under hypothetical interventions on sensitive attributes.
• Empirical results show that these techniques improve fairness and robustness across tasks such as graph node classification, scene graph generation, and multimodal analysis.

Causal graph-based counterfactual debiasing refers to a set of principled machine learning approaches that use explicit causal graphical models to analyze, quantify, and mitigate unwanted bias by leveraging counterfactual interventions. These frameworks aim for predictions, representations, or generative outputs that would remain invariant had protected or nuisance variables been intervened upon in a way specified by the underlying causal graph. The causal approach goes beyond statistical correlations, addressing subtle indirect and networked bias mechanisms that purely associational or group-level fairness metrics can overlook. Counterfactual debiasing, mediated through the formal machinery of causal graphs, intervention calculus, and structured data augmentation, constitutes a major theme in modern fair and robust machine learning.

1. Role of Causal Graphs in Defining and Diagnosing Bias

Causal graphs provide the foundational structure for identifying, reasoning about, and dissecting bias in machine learning systems. Nodes represent observed and latent variables (e.g., features, sensitive attributes, labels), while edges encode hypothesized or learned causal relationships. The presence of paths from protected attributes (e.g., gender, race) to predictions—directly or via mediators such as neighbors’ attributes, metadata, or latent confounders—signals mechanisms through which unfairness may percolate. Distinguishing stable (i.e., causally robust) from unstable or spurious (e.g., selection-driven, environment-specific) paths is fundamental for principled debiasing. For example, a node's prediction in a graph may be affected not just by its own sensitive attribute, but via the sensitive attributes of neighbors and their influence on features or graph structure (Ma et al., 2022). In multimodal settings, confounders can arise from specific modalities or cross-modal interactions (Patil et al., 2023).

Table: Examples of Causal Relationships Leading to Bias

Source	Graph Structure	Bias Mechanism
Node classification in graphs	Node SAs, neighbor SAs	Direct and indirect influence via social context (Ma et al., 2022)
Relation extraction	Entity mentions	Shortcut paths from entity names to label (Wang et al., 2022)
Multimodal classification	Metadata → Output	Shortcut/selection bias via device/site (Koo et al., 25 Oct 2025, Patil et al., 2023)
Text summarization	Prior/irrelevant info	Language/irrelevancy bias ($P \to Y$, $R \to Y$) (Dong et al., 2023)

2. Formalization of Counterfactual Debiasing with Causal Graphs

The central concept underlying causal graph-based counterfactual debiasing is counterfactual invariance: a desired output (prediction, representation, generated data) should be invariant to hypothetical interventions (do-operations) on protected or biased variables, as specified by the causal graph. This can be formalized as:

$$P\left(\hat{Y}_{A \gets a}(U) = y \mid \mathcal{X} = \mathbf{x}, A = a \right) = P\left(\hat{Y}_{A\gets a'}(U) = y \mid \mathcal{X} = \mathbf{x}, A = a \right) \quad \forall\, a, a', y [2205.13972]$$

For graph domains, this extends to interventions on the sensitive attributes of a node and its neighbors, and to the features or even the connectivity structure (Ma et al., 2022).

Counterfactual debiasing practitioners leverage the structural equations and d-separation properties implied by the graph to:

• Identify vulnerable (unstable, non-transportable) paths (Subbaswamy et al., 2018)
• Select or synthesize counterfactual examples where sensitive attributes (and possibly mediators or confounders) are intervened upon (Ma et al., 2022, Liu et al., 22 Mar 2025, Guo et al., 2023)
• Quantify and subtract the estimated effect (often using difference-in-prediction or distance in embedding space) between factual and counterfactual scenarios (Yuan et al., 2022, Wang et al., 2022, Dong et al., 2023, Koo et al., 25 Oct 2025)

3. Core Methods and Algorithmic Implementations

Several general algorithmic templates are recurrent across settings:

3.1 Counterfactual Data Augmentation and Invariance Enforcement

Graph-based frameworks (e.g., GEAR (Ma et al., 2022), CAModule (Liu et al., 22 Mar 2025)) augment the data by simulating one or more counterfactual worlds via direct perturbation or via VAEs/autoencoders conditioned on sensitive attributes. Loss functions—including explicit similarity minimization (e.g., cosine, Euclidean) between representations/predictions in factual versus counterfactual worlds—enforce the desired causal invariance. For example:

$$\mathcal{L}_f = \frac{1}{|\mathcal{V}|} \sum_{i \in \mathcal{V}} [(1-\lambda_s) d(\mathbf{z}_i,\mathbf{z}_i') + \lambda_s d(\mathbf{z}_i, \underline{\mathbf{z}}_i)]$$

where factual and counterfactual representations $$\mathbf{z}_i, \mathbf{z}_i', \underline{\mathbf{z}}_i$$ correspond to original, self-perturbed, and neighbor-perturbed sensitive attributes (Ma et al., 2022).

3.2 Causal-Graph-based Selection of Stable Features

When structural knowledge is incomplete, feature sets can be constructed by including only those features provably not causally downstream of any sensitive attribute in the (possibly partial) causal graph, using efficient algorithms for determining definite descendants in MPDAGs (Zuo et al., 2022).

3.3 Explicit Confounder Modeling and Subtraction

Multimodal and graph models may learn low-dimensional confounder representations (via autoencoders or information minimization) from model-internal features and subtract their contribution from the final prediction via backdoor adjustment or conditional Total Effect subtraction (ATE, TE) (Patil et al., 2023, Koo et al., 25 Oct 2025). In text and vision, counterfactual representations may be constructed via adversarial fine-tuning such that representations become invariant to targeted concepts (Feder et al., 2020).

3.4 Graph-based Logit or Representation Adjustment

By parameterizing adjustment modules as functions of distributions over objects, pairs, co-occurrences, and relationships, debiasing can be targeted at the triplet- or higher-order level, as opposed to global class or feature statistics (Liu et al., 22 Mar 2025).

4. Empirical Findings and Effectiveness

Causal graph-based counterfactual debiasing methods are empirically validated across modalities and domains:

• Graph node classification: GEAR achieves the lowest median counterfactual flip rates ($\delta_{CF}$) and $R^2$ dependency on group features, often approaching zero, without significantly sacrificing task accuracy (Ma et al., 2022).
• Scene graph generation: CAModule attains state-of-the-art mean and zero-shot recall, attributable to triplet-level causally derived corrections (Liu et al., 22 Mar 2025).
• Multimodal classification/sound analysis: Counterfactual plus adversarial approaches yield superior out-of-distribution robustness relative to unimodal and standard multimodal models (Koo et al., 25 Oct 2025, Patil et al., 2023).
• Text summarization and stance detection: Counterfactually estimated corrections, both explicit and implicit, improve factual consistency and generalize to hard, bias-breaking test sets (Dong et al., 2023, Yuan et al., 2022).
• Practicality: Methods scale to real-world benchmarks and are robust to ablation and hyperparameter variation. Causal graph-guided augmentation and adjustment are computationally tractable with local subgraph selection and parameterized adjustment modules.

5. Structural and Theoretical Innovations

Key advances enabling robust counterfactual debiasing include:

• Precise generalization of fairness definitions: From individual-level counterfactual fairness (node-level, text-level) to graph and multimodal settings including neighbor, pairwise, or confounder influences (Ma et al., 2022, Patil et al., 2023).
• Counterfactual effect decomposition: Total Effect, Natural Direct Effect, and Total Indirect Effect computations for disaggregating bias sources (Koo et al., 25 Oct 2025, Yuan et al., 2022, Dong et al., 2023).
• Causal graph-completion under partial knowledge: Theoretically optimal fair prediction shown to be possible with only summary graphical information if root-node conditions on SAs are met (Zuo et al., 2022).
• Empirical stress testing for sensitivity to unmeasured confounding: Efficient algorithms provide explicit bounds on how fairness claims degrade with plausible structural misspecification (Kilbertus et al., 2019).

Table: Representative Mathematical Formalisms

Notion	Formula
Graph Counterfactual Fairness	$$P((Z_i)_{S\leftarrow \mathbf{s}'})=P((Z_i)_{S\leftarrow \mathbf{s}''})$$ (Ma et al., 2022)
Fairness loss (GEAR)	$$\mathcal{L}_f = \frac{1}{|\mathcal{V}|} \sum_i [(1-\lambda_s)d(\mathbf{z}_i,\mathbf{z}_i')+\lambda_s d(\mathbf{z}_i,\underline{\mathbf{z}}_i)]$$
Counterfactual adjustment (CORE)	$$Y_{\mathrm{final}} = Y_x - \lambda_1Y_{\bar{x},e} - \lambda_2 Y_{\bar{x}}$$
Effect decomposition (RSC)	TE $= Y_{t,m} - Y_{t^*,m^*}$; NDE $= Y_{t,m^*} - Y_{t^*,m^*}$; TIE $= Y_{t,m} - Y_{t,m^*}$

6. Impact and Outlook

Causal graph-based counterfactual debiasing has demonstrably advanced the state of fair and robust machine learning:

• It formally unifies and generalizes fairness, robustness, and OOD generalization via a principled causal lens.
• The reliance on explicit graph structure emphasizes the centrality of domain knowledge and identifies when and to what degree group-level or associative fairness metrics can stand in for counterfactual guarantees (Anthis et al., 2023).
• The approach is adaptable, modular, and compatible with emergent architectures (GNNs, LLMs, deep generative models) and edge cases including partial graph knowledge, unknown or latent confounders, and complex multi-agent or multimodal contexts.

Limitations include the need for at least partial causal graph specification or learnability, computational scalability under dense or high-dimensional graphs, and residual sensitivity to unmeasured confounders. However, tools for sensitivity analysis (Kilbertus et al., 2019), partial graph inference (Zuo et al., 2022), intervention-efficient modeling (Liu et al., 22 Mar 2025, Ma et al., 2022), and downstream domain adaptation (Kher et al., 17 Feb 2025) mitigate these issues, defining a robust foundation for ethical and generalizable machine learning driven by causal reasoning.

7. References and Key Contributions

• Learning Fair Node Representations with Graph Counterfactual Fairness (Ma et al., 2022): Formalizes graph counterfactual fairness and presents a practical framework for achieving it.
• Should We Rely on Entity Mentions for Relation Extraction? Debiasing Relation Extraction with Counterfactual Analysis (Wang et al., 2022): Proposes inference-time, model-agnostic counterfactual subtraction for RE.
• Empowering Multimodal Respiratory Sound Classification with Counterfactual Adversarial Debiasing for Out-of-Distribution Robustness (Koo et al., 25 Oct 2025): Advances multimodal debiasing through graph-guided counterfactual and adversarial techniques.
• A Causal Adjustment Module for Debiasing Scene Graph Generation (Liu et al., 22 Mar 2025): Introduces mediator-based causal structures and efficient per-triplet adjustment.
• Counterfactual Fairness with Partially Known Causal Graph (Zuo et al., 2022): Demonstrates fair prediction under structural ambiguity via efficient ancestral algorithms.
• Debiasing Graph Neural Networks via Learning Disentangled Causal Substructure (Fan et al., 2022): Develops disentanglement and counterfactual synthesis for debiasing and interpretability in GNNs.

These frameworks, and others, collectively demonstrate the power, flexibility, and practical necessity of integrating causal graphs and counterfactual reasoning for state-of-the-art debiasing in high-stakes machine learning contexts.