SHAP (SHapley Additive exPlanations)

The sum of all SHAP values for a specific prediction equals the difference between the model's output for that instance and the average model output (the base value). This guarantees the explanation is a complete, additive decomposition of the prediction.

• Definition: f(x) = base_value + sum(SHAP_values)
• Practical Impact: If a CTR model predicts a 12% click probability and the base rate is 5%, the SHAP values for all features will sum to exactly +7%. There is no unexplained variance.

If a feature is missing or has no influence on the prediction, its SHAP value is guaranteed to be zero. This property ensures that features which do not contribute to a model's output are not arbitrarily assigned importance.

• Mechanism: A feature absent from the coalition of inputs receives zero marginal contribution.
• Example: In a CTR model, if a new 'device_type' feature is added but the model learns to ignore it, its SHAP value will consistently be zero across all predictions, preventing analysts from chasing false signals.

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 will not decrease. This ensures that explanations are logically aligned with model behavior.

• Formal Logic: If f_x(S ∪ {i}) - f_x(S) >= g_x(S ∪ {i}) - g_x(S) for all subsets S, then SHAP_i(f) >= SHAP_i(g).
• Significance: This property uniquely distinguishes SHAP from other attribution methods like LIME or DeepLIFT, which can violate consistency and produce misleading feature rankings when models are retrained.

The global property that the average magnitude of a feature's SHAP values across a dataset corresponds to its overall importance to the model. This allows for both local, per-prediction explanations and global feature importance summaries.

• Global Aggregation: Mean absolute SHAP value provides a robust, model-agnostic feature importance metric.
• Use Case: Data scientists use global SHAP bar charts to prune low-importance features from a CTR prediction pipeline, reducing inference latency without sacrificing AUC. This directly connects local explanations to global model optimization.

SHAP values decompose the contribution of feature crosses in models like Field-aware Factorization Machines (FFM). By isolating the interaction effect between, for example, user_age_group and item_category, data scientists can verify if the model has learned a spurious correlation or a genuine behavioral pattern. This prevents over-reliance on brittle co-occurrences that fail when user demographics shift.

Position bias systematically inflates CTR for top-ranked items. SHAP can isolate the marginal contribution of the display_position feature. If position dominates the prediction while item_relevance features have near-zero SHAP values, the model is exploiting layout rather than user preference. This quantifies the exact corrective offset needed for unbiased ranking.

For new items with no interaction history, SHAP reveals which content-based features (e.g., brand, price_tier, description_embedding) the model relies on. If the brand feature has an outsized SHAP value for a new product, it indicates the model is generalizing from brand reputation. This transparency validates whether the fallback logic is reasonable or requires additional contextual signals.

In Multi-gate Mixture-of-Experts (MMoE) architectures predicting both CTR and Conversion Rate (CVR), SHAP can be computed per-task. This allows fairness auditors to check if a protected attribute like user_region has a disproportionately high negative SHAP value for the CVR task but not the CTR task, revealing a hidden bias in the conversion prediction pathway that requires mitigation.

Train-serving skew often manifests as a feature having drastically different SHAP distributions offline versus online. By computing SHAP on a sample of production logs and comparing it to the training set SHAP, engineers can pinpoint the exact feature whose distribution has shifted. A sudden increase in the SHAP magnitude for session_duration online, for instance, signals a change in user engagement patterns that requires model retraining.

In a Deep Interest Network (DIN), the attention weights highlight which historical behaviors are relevant. SHAP provides a complementary, game-theoretic view by showing the final impact of those behaviors on the prediction. If a user's past click on a sports_shoe gets high attention but a negative SHAP value for a running_shoe candidate, it suggests the attention mechanism correctly identified relevance, but the downstream layers penalized the cross-category match.

A set of techniques that assign a score to input features based on their predictive utility. While SHAP provides game-theoretic consistency, other methods offer speed advantages.

• Gini Importance: Measures how often a feature is used for splitting in tree-based models, biased toward high-cardinality features.
• Permutation Importance: Measures the drop in model performance when a feature's values are randomly shuffled, breaking its relationship with the target.
• SHAP Difference: Unlike Gini or Permutation, SHAP values decompose a single prediction into feature contributions, not just global averages.

A precursor to SHAP that explains individual predictions by learning a locally faithful, interpretable surrogate model around the prediction of interest.

• Mechanism: Perturbs the input instance, observes the black-box model's output, and fits a simple linear model weighted by proximity to the original instance.
• Key Limitation: LIME's explanations are not guaranteed to be globally consistent; the same feature can have different importance in two identical instances due to sampling variance.
• SHAP Advantage: SHAP values satisfy Shapley axioms like consistency, ensuring that if a model changes so a feature contributes more, its SHAP value never decreases.

A global visualization tool that shows the marginal effect of one or two features on the predicted outcome, averaged over the dataset.

• Calculation: For each value of a target feature, replaces that feature's value for all instances and averages predictions, marginalizing over the distribution of other features.
• Critical Assumption: Assumes the feature of interest is independent of all other features. Violations produce unrealistic data points and misleading averages.
• SHAP Complement: SHAP dependence plots offer a more granular view by revealing interaction effects and the variance of feature impact across instances, not just the mean.

A deep learning attribution method designed for differentiable models like neural networks, satisfying the completeness axiom that attributions sum to the prediction difference from a baseline.

• Path Integral: Accumulates gradients along a straight-line path from a neutral baseline input (e.g., a black image or zero embedding) to the actual input.
• Axiomatic Match: Satisfies Sensitivity and Implementation Invariance, making it functionally equivalent to Aumann-Shapley values for continuous models.
• SHAP Connection: Deep SHAP implementations like DeepLIFT can be viewed as an efficient approximation of Integrated Gradients, combining the speed of backpropagation with Shapley value axioms.

A high-performance algorithm that computes exact SHAP values for tree ensemble models like XGBoost, LightGBM, and Random Forests in polynomial time instead of exponential.

• Mechanism: Tracks the proportion of all possible feature subsets flowing down each branch of the tree, computing conditional expectations directly from the tree structure.
• Performance: Reduces complexity from O(2^N) to O(TLD^2), where T is trees, L is max leaves, and D is max depth, making it feasible for production CTR models with hundreds of features.
• Interaction Detection: TreeSHAP can also compute SHAP interaction values, quantifying pairwise feature synergies that drive clicks, such as the interaction between user device type and time of day.

The original model-agnostic implementation of SHAP that uses a weighted linear regression to approximate Shapley values for any black-box model.

• Approach: Samples feature coalitions, evaluates the model with features either present or masked, and solves a regression where coalition weights are defined by the Shapley kernel.
• Trade-off: Provides theoretical guarantees for any model type but requires 2^M samples for exact results, making it computationally prohibitive for high-dimensional CTR feature spaces.
• Practical Use: Best suited for explaining small subsets of features or validating faster model-specific methods. For deep CTR models with thousands of embedding features, use Deep SHAP or Integrated Gradients instead.