Total Correlation of Gaussian Pair

Problem

Return the total correlation in bits of a bivariate Gaussian with correlation coefficient rho:

TC = -0.5 * log2(1 - rho^2)

The total correlation is the KL divergence from the joint to the product of its marginals.

Hint

Uncorrelated Gaussian variables carry no total correlation.

case 1

in: [0]

expected: 0

case 2

in: [0.5]

expected: 0.2075187496394219

case 3

in: [0.9]

expected: 1.1979643381655698

case 4

in: [0.8]

expected: 0.7369655941662064

Starter codePython

import math
def total_correlation_gaussian(rho):
    # Your code here
    pass

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