Bias-Variance Tradeoff: The U-Shaped Test Error

Model Flexibility: 5
Test MSE at flex =
0.18
← Minimum (optimal)
Training MSE at flex =
0.25
Decomposition
σ² (noise): 0.06
Bias²:
Variance:
Test MSE (U-curve)
Train MSE
Irreducible σ²
Bias²
Variance
At flex=10: Train MSE→0 but Test MSE is high — overfitting!
Optimal: Bottom of the U (flex≈5)