Q1: If SHAP Tests Prediction with Only One Feature, How Does It Handle the Other Two?
SHAP doesn’t simply set the other features to 0. Instead, it marginalizes them, meaning it replaces them with their expected (average) value from the dataset.
🔹 Example: Suppose we have 3 features in an XGBoost model predicting loan approval:
- Income
- Credit Score
- Age
Now, to estimate SHAP for Income, SHAP asks:
"How does the prediction change when we include Income versus when we exclude it?"
To exclude Income, SHAP replaces it with a typical value from the dataset (not 0, because that could be unrealistic). This is done in two ways:
1️⃣ Mean Imputation: Replace missing features with their average.
2️⃣ Conditional Expectation: Replace missing features with values drawn from similar data points.
💡 Example Calculation:
- Suppose Income = $50K, Credit Score = 750, and Age = 30.
- If we remove "Income", we use an expected Income value, say $45K, based on other people with similar Credit Scores & Age.
- Then, the model predicts without using the real "Income" value.
So, instead of setting missing features to 0, SHAP replaces them with realistic values.
Q2: What Does It Mean by Testing Different Orders of Features?
🔹 Why does SHAP check different feature orders?
Imagine we want to measure how much "Income" contributes to a loan approval decision. But the contribution of Income depends on whether we already know the Credit Score.
- If we first add Income, the model might increase the approval probability a lot.
- If we first add Credit Score, then adding Income later might increase the probability only a little (since Credit Score already explained much of the variation).
How SHAP Handles This?
SHAP calculates the contribution of each feature across all possible feature orders and averages the effect.
🔹 Example Feature Orders Tested:
1️⃣ Income → Credit Score → Age
2️⃣ Credit Score → Income → Age
3️⃣ Age → Income → Credit Score
4️⃣ ... (All possible orders)
💡 Why is this important?
- Some features might appear more or less important depending on whether other features were added first.
- By averaging over all possible orders, SHAP gives a fair contribution score to each feature.
Final Summary
✅ SHAP does not set missing features to 0 but replaces them with typical values from the dataset.
✅ SHAP tests all possible feature orders because feature importance depends on what is already known.
✅ By averaging across orders, SHAP provides a fair, unbiased contribution score for each feature.