How Does SHAP Find the Contribution of Each Feature?

 

SHAP (SHapley Additive exPlanations) is based on game theory. Imagine your model is a team game, where each feature is a player, and the goal is to predict an outcome (e.g., loan approval, fraud detection).

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📌 Step-by-Step Explanation

Step 1: Think of Each Feature as a Player in a Team

Let’s say we have a model predicting loan approval, with these features:

• Income
• Credit Score
• Age

Each feature contributes to the final prediction, just like a player contributes to a team’s success.

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Step 2: Play the Game with Different Combinations of Players

SHAP tests different combinations of features by adding or removing them from the model and checking how much they change the prediction.

Features Used	Model Prediction (Loan Approval %)
No features (baseline)	50%
Income only	70%
Income + Credit Score	85%
Income + Credit Score + Age	90%

Now, SHAP calculates how much each feature increased the prediction.

• Income alone increased approval from 50% → 70% (+20%).
• Credit Score further increased it from 70% → 85% (+15%).
• Age added a smaller increase from 85% → 90% (+5%).

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Step 3: Average the Contribution Across All Possible Orders

SHAP doesn’t just test one order of features. It tries all possible orders and averages the contributions.

Example orderings: 1️⃣ Income → Credit Score → Age
2️⃣ Credit Score → Income → Age
3️⃣ Age → Income → Credit Score
... (all possible ways)

By doing this, SHAP finds the true average contribution of each feature regardless of order.

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🚀 Final Formula (Not Too Math-Heavy)

For each feature $X_i$, SHAP computes:

$$SHAP(X_i) = \sum \left[ \text{(Model prediction with feature)} - \text{(Model prediction without feature)} \right]$$

It averages this over all possible feature orderings.

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📌 Key Takeaways

✅ SHAP = How much a feature changed the prediction
✅ Tries all combinations of features to avoid bias
✅ Averages contributions from different feature orderings
✅ Higher SHAP value = More important feature

Would you like a real example with SHAP visualizations? 🚀