Causal Shapley Values

Standard Shapley values explain predictions based on observational data distributions, which can be misleading when features are correlated. Causal Shapley Values use a causal graph to simulate interventions.

• Interventional Distribution: Breaks spurious links by setting a feature to a value directly, rather than conditioning on it.
• Spurious Correlation: A feature can receive high importance in standard SHAP simply because it is correlated with a true cause; causal SHAP corrects this by blocking back-door paths.

A specific implementation of Causal Shapley Values that respects the asymmetry of causal relationships. It modifies the characteristic function of the game to reflect the causal graph's structure.

• Causal Mechanism: The value function is defined by the marginal distribution of the outcome after intervening on a subset of features.
• Fair Attribution: Ensures that a feature is only rewarded for its direct causal effect on the output, not for information it passively receives from upstream causes.

A core limitation of standard SHAP is its assumption of feature independence, which is often violated in real-world data. Causal Shapley Values explicitly model dependencies.

• Causal Ordering: By defining a directed acyclic graph (DAG), the method knows which features are parents, children, or confounders.
• Robust Explanations: This prevents the importance score from being diluted or inflated by multicollinearity, providing a more robust and legally defensible explanation for high-stakes decisions.

Causal Shapley Values align naturally with counterfactual fairness definitions. They can decompose a prediction change into causal components that answer 'what if' questions.

• Direct vs. Indirect Effect: The method can separate the direct causal effect of a protected attribute (like race) from its indirect effect through legitimate mediating variables (like education).
• Regulatory Compliance: This granular decomposition is critical for auditing automated decisions under regulations like the EU AI Act, proving that a decision was not based on a prohibited causal pathway.

Computing Causal Shapley Values requires both a trained predictive model and a validated Structural Causal Model (SCM). The process involves:

• Graph Validation: The causal graph must be supplied by domain experts or learned via causal discovery algorithms.
• Interventional Sampling: For each coalition of features, the algorithm samples from the interventional distribution defined by the SCM, which is computationally more intensive than marginal sampling in standard SHAP.
• Tools: Libraries like DoWhy and CausalML provide implementations that integrate with popular SHAP frameworks.

In a model predicting disease risk, a standard SHAP analysis might assign high importance to a biomarker that is merely a symptom of an underlying genetic cause. Causal Shapley Values correct this.

• Scenario: A genetic mutation (unmeasured) causes both a high biomarker level and the disease.
• Standard SHAP: Rewards the biomarker heavily because it is predictive.
• Causal SHAP: Identifies that intervening on the biomarker does not change the disease risk, correctly assigning zero causal importance to the symptom and directing resources to the root cause.

The game-theoretic precursor to Causal Shapley Values. This concept fairly distributes the 'payout' (prediction) among 'players' (features) by calculating the average marginal contribution of a feature across all possible coalitions.

• Coalition Logic: Evaluates model output with and without a feature.
• Fairness Axioms: Satisfies efficiency, symmetry, dummy, and additivity properties.
• Limitation: Standard Shapley values assume features are independent and ignore the data-generating process, leading to unrealistic perturbations.

The mathematical backbone enabling Causal Shapley Values. An SCM defines the directed functional relationships between variables, allowing the model to distinguish between mere statistical association and true cause-effect mechanisms.

• Structural Equations: Define how each variable is generated from its direct causes.
• Causal Graph: A Directed Acyclic Graph (DAG) encoding qualitative assumptions.
• Interventional Queries: Enables the do-operator to simulate physical interventions, not just passive observations.

A unified framework of additive feature attribution methods that approximates Shapley values for practical machine learning. KernelSHAP and TreeSHAP are specific implementations.

• Additive Property: Explanation is a linear sum of feature effects.
• Local Accuracy: The sum of feature attributions equals the model output.
• Causal Limitation: Standard SHAP masks features using marginal distributions, which can break causal dependencies and assign importance to non-causal proxies.

Explanations that answer 'What if?' questions by identifying the minimal change to an input required to flip a model's prediction. Causal Shapley Values complement this by quantifying the causal effect of that change.

• Structural Counterfactuals: Use SCMs to compute the effect of an intervention (e.g., 'What if this applicant had a degree?').
• Diverse Outcomes: Methods like DiCE generate multiple distinct paths to a desired outcome.
• Contrastive Nature: Aligns with human reasoning by comparing the factual world to a hypothetical one.

An axiomatic attribution method for deep networks that computes feature importance by accumulating gradients along a straight-line path from a baseline (e.g., a black image) to the actual input.

• Satisfies Completeness: Attributions sum to the difference between the output and the baseline.
• Implementation Invariance: Two functionally equivalent networks receive identical attributions.
• Causal Gap: Like standard SHAP, it relies on observational gradients and does not model the independent causal mechanisms of the input features.

A global model inspection technique that measures the drop in a performance metric (e.g., accuracy) when a single feature's values are randomly shuffled, breaking its relationship with the target.

• Model-Agnostic: Works with any fitted model.
• Correlation Blindness: Severely inflates importance for correlated features because the model is forced to extrapolate to unrealistic, off-manifold data points.
• Causal Alternative: Conditional permutation importance or Causal Shapley Values address this by respecting the correlation structure defined by the causal graph.