Weighted Gini coefficient in Python

问题

Here's a simple implementation of the Gini coefficient in Python, from https://stackoverflow.com/a/39513799/1840471:

def gini(x):
    # Mean absolute difference.
    mad = np.abs(np.subtract.outer(x, x)).mean()
    # Relative mean absolute difference
    rmad = mad / np.mean(x)
    # Gini coefficient is half the relative mean absolute difference.
    return 0.5 * rmad

How can this be adjusted to take an array of weights as a second vector? This should take noninteger weights, so not just blow up the array by the weights.

Example:

gini([1, 2, 3])  # No weight: 0.22.
gini([1, 1, 1, 2, 2, 3])  # Manually weighted: 0.23.
gini([1, 2, 3], weight=[3, 2, 1])  # Should also give 0.23.

回答1:

the calculation of mad can be replaced by:

x = np.array([1, 2, 3, 6])
c = np.array([2, 3, 1, 2])

count = np.multiply.outer(c, c)
mad = np.abs(np.subtract.outer(x, x) * count).sum() / count.sum()

np.mean(x) can be replaced by:

np.average(x, weights=c)

Here is the full function:

def gini(x, weights=None):
    if weights is None:
        weights = np.ones_like(x)
    count = np.multiply.outer(weights, weights)
    mad = np.abs(np.subtract.outer(x, x) * count).sum() / count.sum()
    rmad = mad / np.average(x, weights=weights)
    return 0.5 * rmad

to check the result, gini2() use numpy.repeat() to repeat elements:

def gini2(x, weights=None):
    if weights is None:
        weights = np.ones(x.shape[0], dtype=int)    
    x = np.repeat(x, weights)
    mad = np.abs(np.subtract.outer(x, x)).mean()
    rmad = mad / np.mean(x)
    return 0.5 * rmad

来源：https://stackoverflow.com/questions/48981516/weighted-gini-coefficient-in-python

标签

python

numpy

gini