SAGE (Shapley Additive Global importancE)

Unlike local methods like SHAP, SAGE provides a single importance score per feature for the entire model. It measures how much each feature contributes to the model's expected predictive performance, such as R-squared or cross-entropy loss, over the whole dataset. This allows for direct comparison of feature value across the entire modeling process.

SAGE applies Shapley values from cooperative game theory to the global explanation problem. Each feature is treated as a player in a coalition, and its value is the average marginal increase in model performance when it joins all possible subsets of other features. This ensures a fair, axiomatically justified distribution of credit.

SAGE correctly handles complex feature interactions by evaluating features in the context of all possible subsets. If two features provide redundant information, SAGE splits the credit between them. If a feature is only useful in the presence of another (a synergistic interaction), SAGE accurately reflects this dependency in its global importance scores.

While Permutation Feature Importance breaks correlations by shuffling one feature at a time, SAGE removes a feature by marginalizing it out using the conditional distribution. This makes SAGE more robust to correlated features and provides a theoretically sound measure of importance that avoids extrapolation into unrealistic data regions.

SAGE defines importance based on a loss function, not just prediction variance. A feature is important if including it reduces the model's expected loss (e.g., mean squared error or log loss). This directly ties feature importance to the business metric the model is optimizing, making it highly relevant for model selection and debugging.

Exact SAGE calculation requires retraining the model on all 2^p feature subsets, which is computationally infeasible. Practical implementations use sampling-based approximations, iteratively sampling random subsets of features and observing the change in model performance when a target feature is included versus excluded.

A model-agnostic global importance measure that quantifies the drop in a model's score when a single feature's values are randomly shuffled. Unlike SAGE, it does not account for feature interactions and can produce misleading results when features are correlated. It is computationally simpler but less theoretically grounded than Shapley-based methods.

A global visualization showing the marginal effect of one or two features on the predicted outcome, averaged over the distribution of all other features. PDPs reveal the functional form of a feature's influence (linear, monotonic, non-linear) but assume feature independence, which can lead to unrealistic data points when features are correlated.

An unbiased alternative to PDPs that handles correlated features reliably. ALE computes the local effect by accumulating average differences in predictions over conditional distributions rather than marginal distributions. This prevents the extrapolation artifacts that plague PDPs when features are not independent.

An extension of Shapley values that incorporates a Structural Causal Model (SCM) of the data-generating process. Standard Shapley values measure associational importance, but causal Shapley values assign importance based on interventional effects. This prevents features that are merely correlated with the outcome from receiving inflated importance scores.

An interpretable model (e.g., a shallow decision tree or linear regression) trained to approximate the predictions of a black-box model. Unlike SAGE, which provides per-feature importance scores, a surrogate model provides a complete, simplified representation of the original model's decision logic, enabling holistic inspection.