Causal SHAP

Unlike standard SHAP which treats all features symmetrically, Causal SHAP requires a directed acyclic graph (DAG) encoding the causal relationships between variables.

• Nodes represent observed features and the target variable
• Edges encode direct causal influence (e.g., education → income)
• The graph distinguishes confounders, mediators, and colliders
• Prevents attributing effect to features that are merely correlated, not causal

Causal SHAP decomposes a feature's total effect into direct and indirect components using Pearl's do-calculus.

• Direct effect: The feature's influence on the prediction holding all mediators fixed
• Indirect effect: Influence transmitted through intermediate causal descendants
• Uses interventional distributions P(Y | do(X=x)) rather than conditional distributions
• Avoids the feature independence assumption that standard SHAP often relies on

Standard SHAP treats feature contributions symmetrically, but causal relationships are inherently asymmetric. Causal SHAP respects this directionality.

• If X → Y causally, attributing effect to Y for predicting X is nonsensical
• The causal ordering constrains which coalitions are valid during Shapley value computation
• Prevents credit assignment to downstream effects when the root cause is upstream
• Essential for root cause analysis in industrial and medical diagnostics

Causal SHAP is critical for algorithmic fairness because it isolates the direct discriminatory effect of protected attributes.

• Distinguishes fair correlation (e.g., via a legitimate mediator) from unfair direct discrimination
• Example: Gender may influence income prediction through occupation choice (potentially fair) vs. directly (potentially biased)
• Enables path-specific counterfactual fairness analysis
• Used in compliance with regulations like the EU AI Act for high-risk automated decisions

Causal SHAP is significantly more computationally intensive than TreeSHAP or KernelSHAP due to the need to respect causal constraints.

• Requires causal discovery or domain-expert-provided DAG as a prerequisite
• Must evaluate the model under interventional distributions for each valid coalition
• The number of valid coalitions is restricted by the partial ordering of the causal graph
• Often combined with sampling-based approximation to remain tractable on high-dimensional data

Causal SHAP provides actionable explanations by identifying which features an individual can realistically change to alter an outcome.

• Standard SHAP may recommend changing a non-manipulable feature (e.g., age)
• Causal SHAP restricts recommendations to ancestral features that causally influence the target
• Generates minimal intervention sets for achieving a desired prediction flip
• Critical for algorithmic recourse in credit scoring, hiring, and medical treatment planning

The foundational causal formulation of SHAP that breaks spurious correlations by explicitly simulating interventions on features. Instead of conditioning on observed values, it estimates the marginal distribution of a feature by sampling from the background dataset, answering 'What would the model predict if we set this feature to a specific value?'. This aligns attributions with Pearl's do-calculus, making it the default choice for causal inference but computationally intensive due to the need to marginalize over all other features.

The standard non-causal SHAP formulation that preserves the natural joint distribution of the data. It estimates missing feature values by conditioning on known features, which means attributions reflect both direct causal effects and spurious associations from confounders. While computationally cheaper and faithful to the data manifold, it can assign importance to features that are merely correlated with the outcome, not causally responsible. This is the default behavior in KernelSHAP and TreeSHAP when feature independence is assumed.

Causal SHAP requires a directed acyclic graph (DAG) encoding the causal relationships between features. This graph defines valid adjustment sets and determines which variables must be controlled for when computing the marginal contribution of a feature. By respecting the back-door criterion, the method blocks non-causal paths and isolates the true causal effect of each feature on the prediction. Tools like DoWhy and CausalNex are commonly used to specify this structural knowledge before computing SHAP values.

A generalization of Shapley values that incorporates causal knowledge by restricting the permissible orderings of features during the marginal contribution calculation. In standard SHAP, all permutations are equally weighted, but asymmetric SHAP assigns zero weight to orderings that violate the causal partial order. This ensures a cause never receives credit for an effect that occurs before it in the causal chain, producing attributions that respect the temporal and causal flow of the data-generating process.

The simplifying assumption that all input features are statistically independent, which is violated in most real-world datasets. Under this assumption, the conditional distribution equals the marginal distribution, making interventional and observational SHAP equivalent. While this dramatically reduces computational cost by avoiding complex conditional density estimation, it produces unrealistic model evaluations by feeding the model impossible feature combinations. Causal SHAP explicitly rejects this assumption to generate physically plausible explanations.

The core statistical challenge in causal SHAP: accurately estimating E[f(x) | x_S] when only a subset of features S is known. Methods include:

• Parametric models: Fit a separate model for each feature subset
• Generative models: Use variational autoencoders or normalizing flows to sample from the conditional distribution
• Empirical nearest neighbors: Approximate conditioning by finding similar instances in the background data Poor estimation here introduces bias into the Shapley values, undermining the causal interpretation.