Split gain with missing feature values

Score a threshold split when some rows have no value

A tree split on a numeric feature x needs a value for every row. Real data has gaps, so the C4.5 approach scores the split on the rows that have a value, then scales the gain by the fraction of rows that are known. Rows with a missing value are sent down both branches later, weighted by how the known rows fell.

Implement fractional_split_gain(x, y, threshold), where x is a 1-D float array that may contain NaN, and y holds integer class labels.

• Let known be the rows where x is not NaN, and let F = |known| / n.
• Left branch: known rows with x <= threshold. Right branch: the other known rows.
• gain = F * (H(parent) - weighted child entropy), where H uses base-2 logs and the parent and children are computed on known rows only.
• Return (gain, p_left), where p_left is the fraction of known rows that went left.

Constraints

• x and y must be 1-D with the same length. Otherwise raise ValueError.
• If every value of x is NaN, raise ValueError.
• A split that sends every known row to one side has gain 0.
• Do not modify the inputs.

Hints