Global vs. Local Explanations

Understanding the predictions of complex gradient boosting models is essential for building trust and effectively deploying them. SHAP (SHapley Additive exPlanations), along with its efficient TreeSHAP variant for tree ensembles, offers a powerful framework for interpreting model behavior. This framework allows for both global and local explanations, and understanding the distinction between these levels is important for comprehensive model interpretation.

Global Model Explanations: The Big Picture

Global explanations aim to describe the overall behavior of the trained model across the entire dataset. They answer questions like:

• Which features have the most significant impact on the model's predictions on average?
• What is the general relationship between a specific feature and the model's output?

The most common way to achieve global interpretability with SHAP is by aggregating the SHAP values for each feature across all instances in a dataset (often the validation or test set). A standard approach is to compute the mean absolute SHAP value for each feature $j$:

$$\text{Global Importance}_j = \frac{1}{n} \sum_{i=1}^{n} |\phi_{ij}|$$

Here, $n$ is the number of instances, and $\phi_{ij}$ is the SHAP value for feature $j$ of instance $i$. Features with higher mean absolute SHAP values are considered more influential overall.

This aggregated importance provides a more reliable measure than traditional feature importance metrics (like gain or split count in tree models), which can sometimes be inconsistent.

Visualizing Global Importance

A SHAP summary plot is a powerful visualization that combines feature importance with feature effects. It plots the SHAP values for each feature for every sample, often using color to represent the original feature value (high/low). This reveals not only which features are important but also the distribution and direction of their impact.

A bar chart showing the mean absolute SHAP values for different features. Higher values indicate greater overall influence on the model's predictions.

Another useful global visualization is the SHAP dependence plot, which shows how the model's output changes as a single feature's value changes, potentially colored by an interacting feature.

Local Model Explanations: Understanding Individual Predictions

While global explanations provide a high-level view, local explanations focus on understanding why the model made a specific prediction for a single instance. They answer questions like:

• For this particular customer, why was their loan application denied?
• What factors contributed most strongly to predicting a high probability of churn for this user?

SHAP values are inherently local. The SHAP value $\phi_{ij}$ for feature $j$ of instance $i$ quantifies the contribution of that feature's value towards pushing the prediction for instance $i$ away from the base value (the average prediction over the training dataset).

The core equation of SHAP links the base value $E[f(X)]$ (average prediction) to the prediction $f(x_i)$ for a specific instance $x_i$ through the sum of SHAP values for that instance:

$$f(x_i) = E[f(X)] + \sum_{j=1}^{M} \phi_{ij}$$

Where $M$ is the number of features. This additive nature means we can directly see how each feature contributed positively or negatively to a single prediction relative to the average.

Visualizing Local Explanations

Tools built around SHAP often provide visualizations like "force plots" to illustrate local explanations. A force plot depicts SHAP values as forces acting upon the base value. Features pushing the prediction higher (positive SHAP values) are shown in one color (e.g., red), while features pushing it lower (negative SHAP values) are shown in another (e.g., blue). The size of the feature's block corresponds to the magnitude of its SHAP value.

Diagram of forces contributing to a single prediction. Features push the prediction away from the base value (average prediction). Red features decrease the prediction, blue features increase it. The final prediction is the sum of the base value and all feature contributions (SHAP values).

Complementary Insights

Global and local explanations are not mutually exclusive; they offer complementary perspectives on model behavior.

• Global explanations are valuable for understanding the model's main drivers, comparing different models, and guiding feature engineering efforts.
• Local explanations are indispensable for debugging unexpected predictions, explaining decisions to stakeholders or customers, assessing fairness for individuals, and building trust in specific outcomes.

By leveraging TreeSHAP with XGBoost, LightGBM, or CatBoost, you can efficiently compute these SHAP values and generate both global summaries and detailed local breakdowns, providing a comprehensive understanding of your gradient boosting models.