Bias vs Variance Lab

Bias vs Variance Clinical Fit Lab

Every ML model makes an error. That error has two sources: Bias (systematic mistakes from oversimplification) and Variance (sensitivity to small changes in training data).

Adjust model complexity and watch both components change live.

The Decomposition

The expected total prediction error can be decomposed mathematically:

Err(x) = Bias² + Variance + Noise Bias² = (E[ŷ] − y_true)² systematic error from wrong assumptions Variance = E[(ŷ − E[ŷ])²] sensitivity to training data fluctuations Noise = irreducible error in the data

These cannot both be minimised simultaneously — this is the Bias-Variance Tradeoff.

Clinical Analogy

High Bias (Underfitting): Using only age to predict all cancer risk — ignores BMI, glucose, family history. Systematically wrong for every patient.

High Variance (Overfitting): Memorising every outlier in training data — a rare elderly patient with low BMI "teaches" the model that all elderly patients are low-risk.

Optimal model: — Polynomial degree 3-4 fits the true non-linear clinical signal — Degree 1 = underfits (high bias) — Degree 9+ = overfits (high variance)

⚖️ Ethical Reality

High-variance models overfit to majority-group noise and erase minority-group signals. A model trained mostly on male patients may appear accurate on average but be dangerously high-bias for female patients — whose patterns it never learned.

① Model Complexity

Polynomial Degree3

1 = linear (high bias) · 12 = very complex (high variance)

Noise Level (σ)1.5

Irreducible measurement noise in data

② Error Decomposition

Total Error = Bias² + Variance + Noise
— = — + — + —

—

Bias²

—

Variance

—

Noise

Error Composition

🔴 Bias²🔵 Variance⬜ Noise

③ Model Diagnosis

Clinical Fit Status

UNDERFITTING

What this means clinically

—

Training MSE

—

Test MSE

④ Model Fit — training points (white) · true signal (green dashed) · fitted curve (gradient) · degree shown in title

⑤ Bias-Variance Tradeoff — current complexity marked with yellow dot