A flowchart that learns itself. At each step, pick the yes/no question that best PURIFIES the groups — the one that most reduces the mixing of classes — then repeat on each branch. The plane gets carved into axis-aligned boxes, each voting for a class. It’s the readable classifier: you can literally trace why. Slide the depth and watch the boxes sharpen.
A decision tree recursively splits the data on the feature/threshold that maximizes INFORMATION GAIN — the reduction in impurity (entropy H = −Σp log p, or Gini) weighted by child sizes. Each internal node is a yes/no test; each leaf predicts the majority class of the points that reach it, carving feature space into axis-aligned regions. It is interpretable (you can read the path) but prone to OVERFITTING as depth grows, which pruning and ensembles ([[the-random-forest]]-style) address. A fail-loud self-check throws unless a perfect split drops weighted entropy toward zero (positive info gain). ◆ real machine learning, node-verified.
Greedy, axis-aligned splits shown; a single deep tree overfits (memorizes noise) — real systems limit depth or average many trees. The info-gain criterion and entropy drop are exact.