Partition Function Gradient

Problem

Return the gradient of the log-partition function with respect to the natural parameter, which equals the expected sufficient statistic:

E[T] = sum_i t_i * exp(eta * t_i) / Z

Hint

The gradient of A(eta) = ln Z(eta) is the mean of the sufficient statistic.

case 1

in: [0,[1,2,3]]

expected: 2

case 2

in: [1,[0,1]]

expected: 0.7310585786300049

case 3

in: [2,[-1,0,1]]

expected: 0.8509370922208681

case 4

in: [-0.5,[0,2]]

expected: 0.5378828427399902

Starter codePython

import math
def partition_gradient(eta, t_values):
    # Your code here
    pass

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