MediumCalculusca-230

Jensen Gap Estimate

Problem

For the convex function f(x) = e^x, Jensen's inequality gives E[f(X)] >= f(E[X]), with equality for constant samples.

The gap is E[exp(X)] - exp(E[X]). Given a list of samples, return the empirical gap.

Hint

The gap grows with the variance of the samples for a strictly convex function.

case 1

in: [[0,0]]

expected: 0

case 2

in: [[0,1]]

expected: 0.21041964352939435

case 3

in: [[1,1]]

expected: 0

case 4

in: [[0,2]]

expected: 1.4762462210062801

Starter codePython

def jensen_gap(samples):
    # Your code here
    pass

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