The Bias-Variance Trade-Off

Understanding Overfitting

Simulation Controls

Linear Non-Linear Highly Curvy
Linear (1 df) 5 df High (25 df)
Low 4.0 High

Bias-Variance Rules

  • Training Error (Gray): Always decreases as flexibility increases. The model "memorizes" the specific training points.
  • Test Error (Red): Initially decreases as bias drops, but eventually increases as variance dominates.
  • Irreducible Error: The golden dashed line. No model can ever perform better than this.

Fitted Model (f̂*) vs. Truth (f)

MSE Curve Comparison