DeepAR Gaussian NLL

Problem

Compute the mean Gaussian negative log likelihood used by DeepAR: 0.5 * (ln(2*pi) + 2*ln(sigma) + (y - mu)^2 / sigma^2), averaged over observations.

Return 0.0 for empty observations or non-positive sigma.

Hint

DeepAR learns mu and sigma at each step and minimizes this loss.

case 1

in: [[0],0,1]

expected: 0.9189385332046727

case 2

in: [[1],0,1]

expected: 1.4189385332046727

case 3

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

expected: 1.612085713764618

case 4

in: [[5],5,0]

expected: 0

Starter codePython

import math
def deepar_gaussian_nll(observations, mu, sigma):
    # Your code here
    pass

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