SHAP (SHapley Additive exPlanations)

The sum of all feature attributions equals the difference between the model's output for a specific instance and the average model output. This property guarantees that the explanation is faithful to the original model's prediction.

• Additive: f(x) = base_value + sum(SHAP_values)
• Ensures the prediction is fully decomposed into feature contributions.
• Also known as efficiency in game theory.

A feature that is structurally missing or has a value of zero in the input must receive an attribution of exactly zero. This prevents the explanation from assigning artificial importance to features that did not participate in the prediction.

• Enforces sparsity in explanations.
• Critical for models with sparse inputs like TF-IDF vectors.
• Guarantees that a non-participant gets no credit.

If changing a model so that a feature has a larger impact on the prediction, the SHAP value for that feature cannot decrease. This property ensures that attribution is monotonic with respect to model changes.

• Prevents counter-intuitive attribution shifts.
• Holds across different model architectures.
• A core differentiator from methods like LIME.

If two features contribute identically to every possible subset of other features, they must receive identical SHAP values. This ensures fairness in attribution, preventing arbitrary bias toward one feature over another.

• Based on the game-theoretic principle of equal treatment.
• Essential for detecting multicollinearity effects.
• Guarantees that interchangeable features are valued equally.

For ensemble models like Random Forests or Gradient Boosted Trees, the SHAP value for the ensemble is the average of the SHAP values from each individual tree. This allows for global model interpretation by aggregating local explanations.

• Enables decomposition of complex ensembles.
• Directly links local explanations to global feature importance.
• Computationally efficient via TreeSHAP.

A natively transparent architecture whose internal logic can be directly understood without post-hoc tools like SHAP. The trade-off is often between accuracy and interpretability.

• Glass-box models: Decision trees, GAMs, linear regression
• Black-box models: Deep neural networks, ensembles (require SHAP)
• SHAP bridges the gap by explaining black-box outputs with a theoretically grounded additive model

Quantitative measures evaluating model bias across demographic groups. SHAP values are critical for fairness debugging by identifying which features drive disparate outcomes.

• Demographic Parity: Equal positive prediction rates across groups
• Equalized Odds: Equal error rates across groups
• SHAP can decompose bias into individual feature contributions for root-cause analysis