Oblique split gain

Score a split along a slanted direction

An axis-aligned tree asks one question per node: is feature j at most t? An oblique tree asks about a linear combination instead: is w . x + b <= 0? That lets one node cut a diagonal boundary that would otherwise need a staircase of splits.

Implement oblique_split_gain(X, y, w, b) that scores this split with Gini impurity.

• X is an n by d float matrix, y holds integer labels of length n, w has length d, and b is a scalar.
• Left branch: rows where X @ w + b <= 0. Right branch: the rest.
• Return G(parent) - (n_left / n) G(left) - (n_right / n) G(right), where G = 1 - sum_c p_c^2.

Constraints

• X must be 2-D, w must have length d, and y must have length n. Otherwise raise ValueError.
• w must not be the zero vector. Raise ValueError in that case, because the direction is undefined.
• An empty child contributes zero impurity.
• Do not modify the inputs.

Hints