Every supervised model must choose how much it trusts the training data it happens to see. Here a polynomial curve is refit to several independently noisy samples of the same underlying function. Each resample is stacked along the depth axis so you can watch, in 3D, how tightly (or loosely) the fitted curves agree with one another.
The bias-variance decomposition of squared error was formalised by Geman, Bienenstock and Doursat (1992). It explains why a "perfect" fit to training data (zero training error) can still generalise terribly — the model has simply memorised the noise.
Polynomial regression models are refit to several independently noisy resamples of the same underlying function, stacked along depth so you can watch the fitted curves converge or scatter as complexity changes.
Low-degree fits stay nearly identical across resamples but miss the true curve's shape (high bias). High-degree fits chase each sample's noise and diverge wildly from one another (high variance). Total error is lowest in between.
Raise the model complexity slider and watch the orange curves fan out. Increase noise or shrink the training set to see variance grow further. The three bars on the right track bias², variance and total error live.
The bias-variance decomposition, formalised by Geman, Bienenstock and Doursat in 1992, explains why a model with zero training error can still generalise terribly — it has memorised noise rather than signal.