Permutation Feature Importance Lab

Permutation feature importance answers a very concrete question about any already-trained model: how much worse do its predictions get if one input feature is shuffled so it no longer lines up with the sample it belongs to? This simulator fits a real linear-regression model to a synthetic dataset by ordinary least squares, renders every sample as a point in a 3D cloud positioned by its true feature values, and colors each point by the model's prediction error. Choosing a feature and running the permutation test shuffles that column, feeds the mismatched inputs back through the exact same fitted model, and recolors the cloud live — a feature the model actually depends on turns the cloud red, while an irrelevant one barely changes it. Averaging several independent shuffles turns that single noisy read into the stable importance ranking shown in the side panel.