MediumCalculusca-245

Diagonal Gaussian KL Gradient

Problem

For diagonal Gaussians q = N(mu1, diag(v1)) and p = N(mu2, diag(v2)), the KL divergence has gradient with respect to mu1 equal to (mu1 - mu2) / v2, elementwise.

Given mu1, mu2, and the variances v2 of p as lists, return that gradient as a list.

Hint

The mean gradient of the Gaussian KL is the precision-weighted mean difference.

Test cases

case 1

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

expected: [0,0]

case 2

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

expected: [1,2]

case 3

in: [[0,0],[1,1],[2,4]]

expected: [-0.5,-0.25]

case 4

in: [[3,0],[1,0],[0.5,2]]

expected: [4,0]

Starter codePython

def diagonal_gaussian_kl_grad(mu1, mu2, v2):
    # Your code here
    pass

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