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KernelSHAP Expected Output

Run with: go run main.go

Output

KernelSHAP Example
==================

Base Value: 1.4167

Instance: Origin = [0 0 0]
  Prediction: 0.0000
  SHAP Values:
    x0: -0.4792
    x1: -0.8333
    x2: -0.1042
  Local Accuracy: true (diff=0.00e+00)

Instance: Unit x0 = [1 0 0]
  Prediction: 1.0000
  SHAP Values:
    x0: +0.7292
    x1: -0.8333
    x2: -0.3125
  Local Accuracy: true (diff=0.00e+00)

Instance: Unit x1 = [0 1 0]
  Prediction: 2.0000
  SHAP Values:
    x0: -0.4792
    x1: +1.1667
    x2: -0.1042
  Local Accuracy: true (diff=0.00e+00)

Instance: Mixed = [1 1 1]
  Prediction: 4.0000
  SHAP Values:
    x0: +1.0208
    x1: +1.1667
    x2: +0.3958
  Local Accuracy: true (diff=0.00e+00)

Instance: Large x0 = [2 0.5 0.5]
  Prediction: 6.0000
  SHAP Values:
    x0: +4.3333
    x1: +0.1667
    x2: +0.0833
  Local Accuracy: true (diff=0.00e+00)

Effect of Sample Count on SHAP Estimates
-----------------------------------------

Instance: [2.0, 1.0, 0.5]

Samples    SHAP(x0)     SHAP(x1)     SHAP(x2)     Sum
--------------------------------------------------------------
20         +4.3333      +1.1667      +0.0833      5.5833
50         +4.3333      +1.1667      +0.0833      5.5833
100        +4.3333      +1.1667      +0.0833      5.5833
200        +4.3333      +1.1667      +0.0833      5.5833
500        +4.3333      +1.1667      +0.0833      5.5833

Note: Local accuracy is always guaranteed regardless of sample count.
More samples improve the accuracy of individual SHAP values.

Key Points Demonstrated

  1. Model-Agnostic - Works with any model (uses function f(x) = x0² + 2x1 + x0×x2)
  2. Local Accuracy Guaranteed - Constrained regression ensures SHAP values sum correctly
  3. Sample Count - More samples improve individual SHAP value accuracy
  4. Non-Linear Models - Can explain complex interactions (x0×x2 term)

Understanding the Model

The example uses: f(x) = x0² + 2×x1 + x0×x2

  • x0 has quadratic effect (x0²) and interaction with x2
  • x1 has linear effect (coefficient = 2)
  • x2 only contributes through interaction with x0

How KernelSHAP Works

  1. Sample coalitions - Generate random subsets of features
  2. Compute kernel weights - Weight coalitions by Shapley kernel
  3. Evaluate model - For each coalition, mask absent features with background
  4. Solve regression - Fit weighted linear model to get SHAP values
  5. Enforce constraints - Ensure SHAP values sum to (prediction - baseline)