Log-Sum-Exp

Problem

Compute the numerically stable log-sum-exp of a vector:

LSE(v) = m + log(sum(exp(v[i] - m))), where m = max(v)

This avoids overflow for large entries.

Hint

Subtract the maximum before exponentiating, then add it back.

case 1

in: [[0,0]]

expected: 0.6931471805599453

case 2

in: [[1,2,3]]

expected: 3.4076059644443806

case 3

in: [[1000,1000]]

expected: 1000.6931471805599

case 4

in: [[-1,-2]]

expected: -0.6867383124817772

Starter codePython

def log_sum_exp(v):
    # Your code here
    pass

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