MediumCalculusca-342

Forward KL Gradient in q

Problem

The forward KL divergence KL(p || q) = sum_i p_i log(p_i / q_i) has derivative with respect to q_i equal to -p_i / q_i.

Given the discrete distributions p and q, return the gradient vector with respect to q.

Hint

log(p/q) is linear in log q, so only the -log q term differentiates.

case 1

in: [[0.5,0.5],[0.25,0.75]]

expected: [-2,-0.6666666666666666]

case 2

in: [[0.2,0.8],[0.5,0.5]]

expected: [-0.4,-1.6]

case 3

in: [[1,0],[0.4,0.6]]

expected: [-2.5,0]

Starter codePython

def forward_kl_gradient_q(p, q):
    # Your code here
    pass

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