SHAP Values

The sum of all feature attributions must equal the difference between the model's prediction for a specific instance and the average prediction (base value). This property guarantees that the explanation is a complete and faithful decomposition of the individual prediction.

• Mathematical Form: f(x) = φ₀ + Σᵢ φᵢ, where φ₀ is the base value and φᵢ is the SHAP value for feature i
• Audit Requirement: Enables validators to fully reconstruct a model's decision from its constituent parts
• Contrast: Unlike LIME, which fits a local surrogate that may not perfectly match the original prediction, SHAP's local accuracy is mathematically guaranteed

If a feature is missing or has no influence on the prediction, its SHAP value must be exactly zero. This property ensures that irrelevant or absent features do not arbitrarily contribute to the explanation, maintaining the integrity of the attribution.

• Practical Implication: Features that are structurally missing from a transaction (e.g., a missing device ID for a card-present transaction) are assigned zero contribution
• Regulatory Significance: Prevents the model from appearing to rely on data that was not actually used in the decision
• Implementation: Achieved by averaging over subsets that exclude the feature during the Shapley value calculation

If a model changes such that a feature's marginal contribution increases or stays the same regardless of other features present, that feature's SHAP value must not decrease. This property guarantees that a more important feature is never assigned a lower attribution score.

• Model Governance Value: Ensures that if a feature becomes more predictive of fraud after model retraining, its SHAP importance will reflect this change monotonically
• Comparison to Other Methods: Gain-based feature importance methods (like those in tree ensembles) violate this property, potentially ranking a truly important feature lower after model updates
• Stakeholder Trust: Provides a stable, logically consistent ranking of feature importance across model versions

The total sum of SHAP values across all features for a single prediction is exactly the prediction minus the expected value. This is a restatement of local accuracy but emphasizes that SHAP values operate under a fixed 'budget' of explanation, preventing inflation or deflation of importance.

• Interpretation: The base value (expected model output) plus all SHAP values exactly equals the model output f(x)
• Waterfall Visualization: This property enables the intuitive waterfall chart, where each feature's contribution is a step from the base value to the final prediction
• Audit Completeness: Validators can confirm that no unexplained variance remains in any individual decision

If two features contribute identically to the model's prediction across all possible subsets of other features, they must receive identical SHAP values. This property ensures that features with equivalent predictive power are treated equally by the explanation framework.

• Fairness Implication: Prevents arbitrary bias in attribution when two features have identical statistical relationships with the target variable
• Example: If 'transaction_amount' and 'log_transaction_amount' are perfectly correlated and used identically by the model, they receive equal SHAP values
• Model Debugging: Violations of symmetry in practice can reveal unexpected feature interactions or encoding artifacts

While SHAP values are derived from Shapley values in cooperative game theory, the framework is model-agnostic. KernelSHAP provides a model-agnostic approximation, while TreeSHAP and DeepSHAP offer exact, computationally efficient implementations for tree-based models and neural networks respectively.

• KernelSHAP: Works with any black-box model by sampling feature coalitions and fitting a weighted linear model
• TreeSHAP: Computes exact SHAP values in polynomial time for tree ensembles like XGBoost, LightGBM, and Random Forests
• DeepSHAP: Leverages DeepLIFT's linear composition rules to efficiently approximate SHAP for deep neural networks
• Enterprise Flexibility: Allows a single explanation standard across heterogeneous model inventories