Shapley Values

The sum of all feature attributions equals the difference between the model's prediction for a specific instance and the average prediction. This property guarantees completeness—the explanation accounts for the entire prediction output, leaving no residual unexplained variance.

• Additive property: f(x) = ϕ₀ + Σ ϕᵢ where ϕ₀ is the base value and ϕᵢ are Shapley values
• Ensures the explanation is a true decomposition of the prediction
• Critical for regulatory compliance where full accountability is required

If two features contribute identically to every possible coalition, they receive identical Shapley values. This equal treatment property prevents bias in attribution and ensures that features with the same predictive influence are assigned the same importance.

• Eliminates arbitrary ordering effects present in simpler methods
• Guarantees consistent ranking of feature importance
• Essential for auditing models in lending and hiring where fairness is legally mandated

A feature that contributes nothing to the prediction—regardless of which other features are present—receives a Shapley value of exactly zero. This null effect property ensures that irrelevant features do not receive spurious attribution.

• Automatically zeroes out non-predictive variables
• Prevents misleading explanations that highlight noise features
• Useful for feature selection by identifying truly inert inputs

If a prediction is the sum of two separate model outputs, the Shapley value for a feature is the sum of its Shapley values from each model. This linear consistency property enables explanations for ensemble models like random forests and gradient boosted trees.

• Allows decomposition of ensemble predictions into component model contributions
• Ensures explanations remain consistent when models are combined
• Foundational for SHAP's ability to explain any model architecture

Shapley values compute a feature's importance by averaging its marginal contribution across all 2ᴺ possible feature coalitions. For each subset of features, the model's prediction is evaluated with and without the target feature, and the difference is weighted by coalition size.

• Weighting formula: |S|!(n - |S| - 1)! / n! where S is the coalition
• Accounts for feature interactions by considering all possible orderings
• Computationally expensive—exact calculation requires O(2ⁿ) model evaluations

Shapley values are the only attribution method that simultaneously satisfies efficiency, symmetry, dummy, and additivity. This uniqueness theorem, proven by Lloyd Shapley in 1953, provides the theoretical foundation for why SHAP is the gold standard in model explainability.

• No other method can claim this axiomatic completeness
• Provides a defensible mathematical basis for regulatory submissions
• Contrasts with heuristic methods like LIME that lack formal guarantees

The direct computational implementation of Shapley Values for machine learning. SHAP unifies six existing attribution methods under a single game-theoretic framework, assigning each feature an importance value for a specific prediction. In fraud detection, SHAP values explain exactly why a transaction scored 0.92 on a risk model—for example, revealing that transaction amount contributed +0.15 and device fingerprint mismatch contributed +0.40 to the anomaly score. The KernelSHAP variant is model-agnostic, while TreeSHAP provides exact, fast computations for gradient-boosted trees commonly used in anti-fraud systems.

A perturbation-based alternative to Shapley methods that explains individual predictions by locally approximating the black-box model with an interpretable surrogate, such as a sparse linear model or decision tree. LIME generates synthetic samples around the instance being explained and weights them by proximity. While computationally lighter than exact Shapley calculations, LIME's explanations can be unstable—two nearby transactions may yield different explanations due to sampling variance. Fraud analysts often use LIME for rapid, approximate debugging before applying the more rigorous SHAP framework.

A model-specific attribution method designed for deep neural networks that satisfies the completeness axiom—the sum of feature attributions equals the difference between the model's output and a baseline prediction. It computes contributions by integrating gradients along a straight-line path from a baseline input (often a zero-vector or average transaction) to the actual input. In fraud detection, this is particularly useful for explaining recurrent neural networks that process transaction sequences, identifying which specific steps in a payment history triggered the anomaly flag.

Instead of assigning importance scores, counterfactuals answer: 'What would need to change for this transaction to be classified as legitimate?' They identify the minimal set of feature perturbations that flip the model's decision. For a flagged wire transfer, a counterfactual might state: 'If the beneficiary account age were 3 years instead of 2 days, this transaction would not be blocked.' This approach aligns naturally with adverse action reason codes required by financial regulators and provides actionable guidance for investigators reviewing false positives.

A global model inspection technique that measures feature importance by randomly shuffling each feature's values and observing the decrease in model performance. Unlike Shapley Values, which provide local explanations per transaction, permutation importance gives a single ranking of features across the entire validation set. A significant drop in AUC-ROC after shuffling 'transaction velocity' indicates that feature is globally critical. However, this method can be misleading when features are correlated—a limitation that Shapley-based approaches address through coalitional game theory.

A global visualization tool showing the marginal effect of one or two features on the model's predicted fraud probability, averaged over all other features. A PDP for 'transaction amount' might reveal a sharp increase in fraud risk above $10,000. While intuitive for regulators, PDPs assume feature independence—a problematic assumption in financial data where account balance and transaction amount are correlated. The Shapley framework avoids this pitfall by explicitly modeling feature interactions through coalitional marginal contributions.