Build the Root

A decision tree does not pick the first reasonable split—it evaluates every candidate and chooses the winner for the root node.

The splitting process repeats the same recipe at every node:

1. For each feature, generate all midpoint thresholds.
2. For each (feature, threshold) pair, split the data into left and right groups.
3. Compute weighted Gini for that split.
4. Pick the pair with the smallest weighted Gini.

That winning split becomes the node's decision. Impure child groups are split again using the same process.

For each candidate feature and threshold:

$$\text{Weighted Gini} = \frac{n_{\text{left}}}{n} \cdot \text{Gini}(\text{left}) + \frac{n_{\text{right}}}{n} \cdot \text{Gini}(\text{right})$$

The best split minimizes this score:

$$\text{Best split} = \arg\min_{\text{feature},\, t} \;\text{Weighted Gini}$$

If two splits tie, libraries use a consistent tie-breaking rule (often preferring the earlier feature).

On the 8-sample practice dataset, the root node compares every candidate:

Winner: Feature 0, threshold $2.5$, weighted Gini $= 0.1875$.

After this split:

• Right ($x > 2.5$): all class 1 → pure leaf, predict 1
• Left ($x \leq 2.5$): still mixed → recurse and find the next best split

Comparing only one feature or one threshold. A tree must evaluate all features and all midpoints at each node—otherwise it can miss a much better split.

The best split is the (feature, threshold) pair with the lowest weighted Gini. Trees repeat this search at every impure node until stopping conditions apply.

Use the Best Split Finder below to see every candidate ranked on the practice dataset.