SHAP (SHapley Additive exPlanations)

The Symmetry property states that if two features contribute identically to every possible subset of other features, they must receive identical SHAP values. This enforces a fundamental fairness constraint: features are judged solely by their impact, not by arbitrary ordering or naming.

• Core principle: Equal contributions yield equal credit.
• Game theory origin: Symmetric players in a coalitional game receive the same payoff.
• Real-world relevance: Prevents bias in explanation where two correlated, equally predictive features might otherwise be arbitrarily ranked.

The Dummy or Missingness axiom requires that a feature which never changes the model's prediction—regardless of which other features are present—must receive a SHAP value of zero. This prevents spurious importance from being assigned to irrelevant inputs.

• Zero impact = Zero attribution: A feature with no marginal contribution gets no credit.
• Handling missing data: In SHAP, a missing feature is represented by its expected value from the background dataset, and its contribution is correctly set to zero.
• Sanity check: If a random noise column receives a non-zero SHAP value, the explanation method is broken.

The Additivity property states that for a model ensemble (e.g., a Random Forest or a voting classifier), the SHAP value of a feature is the weighted average of its SHAP values from each constituent model. This allows explanations to be cleanly aggregated.

• Ensemble transparency: The global explanation is a mathematically sound combination of sub-model explanations.
• Use case: When auditing a stacked model, you can decompose the final attribution to understand which base learner drove a specific feature's importance.
• Contrast: Many other attribution methods break down or require re-computation when applied to ensembles.

The Consistency property guarantees that if a model is retrained or modified so that a specific feature's marginal contribution increases (or stays the same) for all subsets, that feature's SHAP value will not decrease. This ensures stability and logical monotonicity in explanations.

• Model evolution: As models are updated, feature importance shifts are logically consistent.
• Trust: A feature that becomes strictly more important in a new model version will never be assigned a lower attribution.
• Unique solution: SHAP is the only additive feature attribution method that satisfies Efficiency, Symmetry, Dummy, and Consistency simultaneously.

A model-agnostic implementation that treats the explanation as a weighted linear regression problem. It uses a specially designed Shapley kernel to approximate Shapley values without exhaustive computation over the power set.

• Mechanism: Samples coalitions, fits a local linear model where weights are determined by coalition size.
• Key Insight: The kernel ensures the linear model satisfies the efficiency property at the instance being explained.
• Trade-off: Computationally expensive for high-dimensional data due to sampling requirements.

A model-specific algorithm that computes exact Shapley values for tree-based models in polynomial time (O(TLD^2) where T is trees, L is leaves, D is depth). It exploits the internal structure of decision trees to track feature splits directly.

• Advantage: Orders of magnitude faster than KernelSHAP for XGBoost, LightGBM, and random forests.
• Output: Provides both conditional expectation (observational) and interventional SHAP values.
• Interaction Values: Natively computes pairwise SHAP interaction values without additional sampling.

A high-speed approximation for deep learning models that combines DeepLIFT rules with Shapley value calculations. It uses a compositional approximation where the SHAP values of network components are combined to approximate the full model's attributions.

• Mechanism: Propagates attributions layer-by-layer using linear composition rules.
• Baseline: Requires a carefully chosen background dataset representing missing feature information.
• Limitation: The approximation quality degrades for highly non-linear activation functions and complex skip connections.

A causal interpretation of SHAP that breaks feature correlations by sampling from the marginal distribution. It answers: 'How does the model behave if we actively intervene on this feature?'

• Method: Replaces feature values with random draws from the background dataset, ignoring dependencies.
• Use Case: Essential for fairness auditing and scenarios where causal reasoning is required.
• Contrast: Unlike observational SHAP, it evaluates the model on data points that may lie off the natural data manifold.

A formulation that preserves feature correlations by conditioning on observed values. It estimates missing features using the conditional expectation given the known features, reflecting the model's behavior on the natural data manifold.

• Method: Uses a separate model or non-parametric estimator to impute missing features based on observed ones.
• Use Case: Preferred when explaining predictions on realistic, correlated data where interventions would create implausible feature combinations.
• Challenge: Requires accurate estimation of the conditional distribution, which is computationally intensive.

An extension that incorporates a causal graph (directed acyclic graph) to compute feature attributions respecting the underlying causal structure of the data. It decomposes the total effect into direct and indirect causal pathways.

• Mechanism: Uses Pearl's do-calculus to simulate interventions along causal edges.
• Output: Distinguishes between direct causal effects and spurious associations driven by confounders.
• Application: Critical for policy evaluation and medical treatment effect analysis where causal reasoning is paramount.