Fisher Information 1D

Problem

Compute the Fisher information of a Bernoulli-logistic model with logit z.

Let p = 1 / (1 + exp(-z)); the Fisher information with respect to z is p * (1 - p). Return that value, which peaks at z = 0.

Hint

The Fisher information is the variance of the Bernoulli score.

case 1

in: [0]

expected: 0.25

case 2

in: [1]

expected: 0.19661193324148185

case 3

in: [-2]

expected: 0.1049935854035065

case 4

in: [5]

expected: 0.006648056670790033

Starter codePython

def fisher_information_1d(z):
    # Your code here
    pass

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