Predictive Residual Entropy

Problem

Return the differential entropy in bits of the residual after first-order linear prediction:

h = 0.5 * log2(2 * pi * e * var * (1 - rho^2))

where var is the signal variance and rho the correlation with the predictor. Assume |rho| < 1.

Hint

Better prediction shrinks the residual variance by (1 - rho^2).

case 1

in: [1,0]

expected: 2.047095585180641

case 2

in: [1,0.5]

expected: 1.8395768355412192

case 3

in: [4,0]

expected: 3.047095585180641

case 4

in: [1,0.9]

expected: 0.8491312470150711

Starter codePython

import math
def residual_entropy(var, rho):
    # Your code here
    pass

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