Bias–Variance Decomposition
Expected prediction error splits exactly into three parts: bias² (the average model misses the truth), variance (fits wobble across training sets) and irreducible noise. Pick a true function — sine, cubic or step — set the noise level and training-set size, then choose a model: polynomial regression with a degree slider or k-NN with a k slider. The tool draws 50 independent training sets and fits them all: individual fits appear as faint orange spaghetti, their average as a bold orange curve, the truth as a dashed blue line. Drag the green probe marker to read bias², variance and noise as a stacked bar at that x, and press Sweep to plot the full decomposition against model complexity — the classic U-shaped total error emerges as bias falls and variance rises.
Runs 100% in your browser — models are trained and computed locally on your device.
Read the full guide to this tool
Notes
- For squared loss the decomposition is exact and has no cross terms: E[(y − ŷ)²] = bias² + variance + σ².
- Low-degree polynomials (or large k in k-NN) underfit: high bias, low variance. High degree (or k = 1) overfits: bias vanishes but variance explodes.
- Variance is what regularization, bagging and more data reduce; bias only falls when the model class itself becomes more flexible.
- Runs 100% in your browser — models are trained and computed locally on your device.
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