Hinge Loss Subgradient

Problem

Compute the mean subgradient of the hinge loss with respect to w and b for labels in {-1, +1}.

For each sample with margin y_i * (b + x_i . w) < 1, subtract y_i / n from grad_b and y_i * x_ij / n from grad_w[j]. Return [grad_b, grad_w]; empty X returns [0.0, [0.0] * len(w)].

Hint

Samples with margin at least 1 contribute nothing to the subgradient.

Test cases

case 1

in: [[[1],[2]],[1,-1],[0],0]

expected: [0,[0.5]]

case 2

in: [[[1]],[1],[2],0]

expected: [0,[0]]

case 3

in: [[[1,1],[2,-1]],[1,1],[0,0],0]

expected: [-1,[-1.5,0]]

case 4

in: [[],[],[1,2],0]

expected: [0,[0,0]]

Starter codePython

def hinge_subgradient(X, y, w, b):
    # Returns [grad_b, grad_w]
    # Your code here
    pass

4 test cases · run your code against them in the editor