MediumCalculusca-371

Jensen Gap for Sigmoid Samples

Problem

The Jensen gap is E[f(X)] - f(E[X]). For the sigmoid f and a list of equally weighted samples, compute both the average of the sigmoid values and the sigmoid of the average, then return the gap.

Given the sample list, return E[sigmoid(X)] - sigmoid(E[X]).

Hint

Average the transformed values, then subtract the transform of the average.

Test cases

case 1

in: [[0,2]]

expected: -0.040660039641063794

case 2

in: [[-1,1]]

expected: 0

case 3

in: [[1,1,1]]

expected: 0

Starter codePython

def jensen_gap_sigmoid_samples(samples):
    # Your code here
    pass

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