VAE ELBO

Problem

Compute the evidence lower bound for one example: expected log-likelihood minus the KL term. Here the log-likelihood is the negative sum of squared reconstruction errors and the KL uses log_var, so ELBO = -sum((x - x_hat)^2) - KL.

The signature is vae_elbo(x, x_hat, mu, log_var). Return a scalar.

Hint

Maximizing the ELBO is equivalent to minimizing reconstruction error plus KL.

Test cases

case 1

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

expected: 0

case 2

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

expected: -5

case 3

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

expected: -0.5

case 4

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

expected: -1.3591409142

Starter codePython

import math
def vae_elbo(x, x_hat, mu, log_var):
    # Your code here
    pass

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