Length Bias Correlation

Problem

Measure length bias as the Pearson correlation between rewards and response lengths.

Return cov / sqrt(var_r * var_l) computed with population moments. Return 0.0 when there are fewer than two points or either variance is zero.

Hint

A positive reward-length correlation is the classic signature of length bias.

case 1

in: [[1,2,3],[10,20,30]]

expected: 1

case 2

in: [[3,2,1],[10,20,30]]

expected: -1

case 3

in: [[1,2],[5,5]]

expected: 0

case 4

in: [[1],[2]]

expected: 0

Starter codePython

import math
def length_bias_correlation(rewards, lengths):
    # Your code here
    pass

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