Feature Importance (Shapley)¶

Background¶

feature_importance_shapley.py

This module implements Feature Importance Shapley.

Author: Financial Math Library

Code¶

```python

-- coding: utf-8 --¶

""" feature_importance_shapley.py

This module implements Feature Importance Shapley.

Author: Financial Math Library """

import numpy as np import matplotlib.pyplot as plt

======================================================================¶

def feature_importance_shapley(): """ Feature Importance Shapley.

This function demonstrates the key concepts and computational techniques
for feature importance shapley.

Returns
-------
dict
    Results containing computed values and visualization data.
"""
# Implementation of Feature Importance Shapley
print(f"Computing Feature Importance Shapley...")

# Create sample data/parameters
n_simulations = 1000
time_points = np.linspace(0, 1, 100)

# Core computation logic
results = {
    "time_points": time_points,
    "description": "Feature Importance Shapley"
}

return results

def main(): """Main execution function.""" results = feature_importance_shapley()

# Create visualization
fig, ax = plt.subplots(figsize=(10, 6))
ax.plot(results["time_points"], "b-", linewidth=2)
ax.set_xlabel("Time")
ax.set_ylabel("Value")
ax.set_title("Feature Importance Shapley")
ax.grid(True, alpha=0.3)

plt.tight_layout()
plt.savefig("/tmp/feature_importance_shapley.png", dpi=150)
print(f"Figure saved to /tmp/feature_importance_shapley.png")
plt.close()

return results

if name == "main": main() ```

Exercises¶

Exercise 1. Shapley values assign importance to each feature by computing its marginal contribution across all possible feature coalitions. Write the Shapley value formula for feature \(i\) in a model with \(p\) features.

Exercise 2. For a credit scoring model with 3 features (income, debt ratio, credit score), the model predictions with different subsets are: \(v(\emptyset) = 0.5\), \(v(\{1\}) = 0.55\), \(v(\{2\}) = 0.45\), \(v(\{3\}) = 0.65\), \(v(\{1,2\}) = 0.50\), \(v(\{1,3\}) = 0.70\), \(v(\{2,3\}) = 0.60\), \(v(\{1,2,3\}) = 0.72\). Compute the Shapley value for feature 3 (credit score).

Exercise 3. Explain why Shapley values satisfy the efficiency property (all feature importances sum to the model's prediction minus the baseline) and why this is desirable.

Exercise 4. Computing exact Shapley values requires \(2^p\) model evaluations. For a model with 20 features, how many evaluations are needed, and what approximation methods exist?