Variational Bound Tightness

Problem

Return the gap between the log evidence and the evidence lower bound:

gap = log_evidence - elbo

The gap equals the KL divergence from the variational posterior to the true posterior, so the bound is tight exactly when the gap is zero.

Hint

The ELBO is always at most the log evidence for any variational family.

case 1

in: [10,9]

expected: 1

case 2

in: [0,0]

expected: 0

case 3

in: [-5,-7]

expected: 2

case 4

in: [3.5,3.5]

expected: 0

Starter codePython

def elbo_gap(log_evidence, elbo):
    # Your code here
    pass

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