Global Feature Importance

If a model is retrained or modified such that a feature's marginal contribution increases or stays the same regardless of other features, its global SHAP importance will never decrease. This prevents counter-intuitive ranking reversals.

• Guarantees that improving a feature's true impact is reflected in its importance score
• Eliminates scenarios where a more useful feature is ranked lower after model updates
• Critical for regulatory audits where feature importance must track model logic

The sum of all global feature importances exactly equals the total model output variance explained by the features. No importance is lost or double-counted.

• The global importance of feature i is the mean absolute SHAP value: I_i = mean(|φ_i|)
• Σ I_i = Total Attribution — the budget is perfectly partitioned
• Enables direct comparison: "Feature A is 3x more important than Feature B" is mathematically valid

Features that are structurally missing, constant, or have zero variance across the entire dataset are assigned exactly zero global importance. This property prevents ghost attributions to non-predictive inputs.

• A constant feature (e.g., country='US' for all rows) contributes nothing
• Eliminates false signals from invariant metadata accidentally included in the model
• Ensures feature importance budgets are not diluted by noise variables

Two features that contribute identically to the model's output in all possible coalitions receive identical global importance scores. This enforces fairness in ranking.

• If X1 and X2 are perfectly redundant, they split importance equally
• Prevents arbitrary ranking of collinear features based on index or name
• Reflects the game-theoretic principle that interchangeable players earn equal payoffs

Global SHAP importance is defined purely by the model's input-output behavior, not its internal architecture. The same mathematical framework applies identically to gradient-boosted trees, deep neural networks, and linear models.

• Enables cross-model comparison: "Is feature importance stable across XGBoost and MLP?"
• No access to gradients or weights required for KernelSHAP estimation
• Unifies auditing workflows across heterogeneous model portfolios

Global importance can be extended to SHAP interaction values, which decompose total importance into main effects and pairwise interaction effects. This reveals whether a feature is important alone or only through synergy.

• Φ_{i,i} captures the pure main effect of feature i
• Φ_{i,j} captures the interaction effect between features i and j
• Prevents misattribution: a feature may rank high globally only due to its interaction with a driver feature