In the world of machine learning, model interpretability is paramount. While black-box models, such as deep neural networks or ensemble methods, often outperform simpler models, their predictions can be difficult to interpret. SHAP values, based on game theory, have emerged as a popular method for explaining individual predictions made by complex models. SHAP plots visualize these values.
Background
SHAP values derive from the concept of Shapley values in cooperative game theory. Lloyd Shapley introduced Shapley values to distribute a total payoff among players in a game based on their individual contributions. Similarly, in a predictive model, SHAP values help attribute the prediction output to its input features.
Calculating SHAP Values
For a given instance and a model’s prediction, the SHAP value for a feature is the average difference in the model’s output when considering that feature versus when not considering it, weighed over all possible combinations of features.
Mathematically, for a binary classifier:
\text{SHAP}(i) = \sum_{S \subseteq N \setminus \{i\}} \frac{|S|!(|N|-|S|-1)!}{|N|!} \left[ f(S \cup \{i\}) - f(S) \right]
Where:
is the set of all features.
S is a subset of N that does not include feature i.
f is the predictive model.
The difference f(S∪{i})−f(S) represents the impact of feature when moving from subset S to subset S∪{i}.
Visualization: SHAP Plots
Several types of SHAP plots visualize the impact of features:
- SHAP Summary Plot:
- Provides a bird’s-eye view of feature importance and directionality. Each point represents a SHAP value for a feature and an instance. Features are ordered by importance.
- SHAP Dependence Plot:
- Depicts the relationship between the SHAP value of a feature and the feature’s values. It helps understand how a feature impacts the prediction across its range.
- SHAP Force Plot:
- Represents the contribution of each feature to a particular prediction, showing base values, feature values, and the resultant output.
Advantages of SHAP
- Consistency: If the contribution of a feature value increases, the SHAP value for that feature should not decrease.
- Local Accuracy: The sum of SHAP values for all features should equal the difference between the model’s prediction and the expected prediction.
- Fair Allocation: Symmetry and dummy features are fairly handled, ensuring unbiased feature importance allocation.
Applications
- Model Debugging: Identify which features cause unexpected predictions.
- Regulatory Compliance: In sectors like finance or healthcare, SHAP offers transparency required by regulations.
- Improved Decision Making: Stakeholders can trust and understand decisions made by ML models.
Limitations
- Computational Cost: Computing exact SHAP values can be expensive, especially for complex models and large datasets.
- Interpretation Overhead: While SHAP values enhance transparency, they also introduce a new layer of complexity that stakeholders must understand.
