SHAP

The sum of all SHAP values for a prediction equals the difference between the model's output for that instance and the average model output over the dataset. This guarantees a complete, faithful decomposition of the prediction.

• Mathematical Form: f(x) = φ₀ + Σᵢ φᵢ where φ₀ is the base value (expected model output) and φᵢ is the SHAP value for feature i.
• Practical Impact: No unexplained variance remains. If a model predicts a 90% probability of signal interception and the base rate is 60%, the SHAP values for SNR, frequency drift, and modulation type will sum to exactly +30%.
• Contrast with LIME: LIME approximates this locally but does not guarantee a perfect decomposition, making SHAP the preferred choice for high-assurance RF audits.

A feature that is missing or has no influence on the prediction must receive a SHAP value of exactly zero. This prevents the attribution method from hallucinating importance for irrelevant inputs.

• Mechanism: If a feature is not included in a coalition, its contribution is defined as zero. This is enforced by the Shapley value calculation, not a heuristic.
• RFML Example: In a specific emitter identification (SEI) model, if the I/Q phase noise feature is masked or absent from the input vector, its SHAP value is guaranteed to be 0.0, preventing false attribution to a non-existent signal characteristic.
• Debugging Utility: Non-zero SHAP values for a feature you believe to be irrelevant indicate either a data leakage problem or a spurious correlation learned by the neural network.

If a model changes so that a feature's marginal contribution increases or stays the same regardless of other features, the SHAP value for that feature cannot decrease. This ensures attribution logic remains stable under model retraining.

• Formal Definition: If f_x(S ∪ {i}) - f_x(S) ≥ g_x(S ∪ {i}) - g_x(S) for all subsets S, then φᵢ(f) ≥ φᵢ(g).
• Operational Significance: When you retrain an automatic modulation classification (AMC) model and the cumulant-based feature becomes strictly more important in every possible feature subset, its SHAP value is mathematically guaranteed to increase. This property is unique to SHAP among additive attribution methods.
• Trust Calibration: Consistency allows mission assurance leads to track how feature importance evolves across model versions without worrying about attribution artifacts.

If two features contribute identically to every possible coalition of other features, they must receive identical SHAP values. This enforces fairness in the attribution process.

• Game Theory Origin: In the Shapley value context, players who contribute equally to all coalitions receive equal payouts. This principle maps directly to feature attribution.
• RF Scenario: In a channel estimation neural network, if two pilot subcarriers provide perfectly redundant information about the channel state, they will receive identical SHAP values. This correctly identifies them as interchangeable for the prediction.
• Feature Selection Implication: Symmetry helps identify redundant features in high-dimensional RF datasets, guiding dimensionality reduction without losing interpretability.

The total attribution budget across all features is fixed and exactly accounts for the model's deviation from the baseline. This property is a global extension of local accuracy.

• Aggregation: When SHAP values are averaged across a dataset, the mean absolute SHAP value for each feature provides a global feature importance ranking that sums to the total explainable variance.
• Spectrum Sensing Use Case: In a cyclostationary signal detector, efficiency ensures that the importance scores for the cyclic prefix correlation, symbol rate estimate, and carrier frequency offset collectively account for 100% of the model's decision to flag a signal as LTE vs. 5G NR.
• Regulatory Compliance: Efficiency provides auditors with a closed-form accounting of every factor influencing an automated spectrum access decision, satisfying explainability mandates in cognitive radio systems.