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Best Split Finder

Find the best threshold for splitting a feature to maximize information gain.

Given a list of feature values and corresponding labels, try every midpoint between consecutive sorted unique feature values as a potential split threshold. For each threshold, split the data into left ( $\leq$ threshold) and right ( $>$ threshold) subsets.

Return the threshold that gives the highest information gain, along with the gain value, as a tuple (threshold, gain). Both rounded to 4 decimal places.

If there's no possible split (all values identical), return (None, 0.0).

Example:

Input:

feature_values = [1, 2, 3, 4]
labels = [0, 0, 1, 1]

Output:

(2.5, 1.0)

Reasoning:

First, we sort the unique feature values and find midpoints: $[1, 2, 3, 4]$ has midpoints at $1.5$ , $2.5$ , and $3.5$ .
Then, we calculate the information gain for each midpoint threshold, e.g., for $2.5$ , we split the data into $[1, 2]$ with labels $[0, 0]$ and $[3, 4]$ with labels $[1, 1]$ .
The information gain for $2.5$ is calculated as $IG = H([0, 0, 1, 1]) - \frac{2}{4}H([0, 0]) - \frac{2}{4}H([1, 1]) = 1 - \frac{1}{2} \cdot 0 - \frac{1}{2} \cdot 0 = 1.0$ , which is the highest gain among all midpoints.
Since $2.5$ yields the highest information gain of $1.0$ , the output is $(2.5, 1.0)$ .

Constraints:

feature_values: list of numeric values
labels: list of class labels (same length)
Split: left = values <= threshold, right = values > threshold
Return (best_threshold, best_gain) rounded to 4 decimal places

Editor

Python 3.13.1

Test Results

0/0

Run code to see test results.