Python中更有效的加权基尼系数

根据 https://stackoverflow.com/a/48981834/1840471,这是Python中加权基尼系数的实现：

import numpy as np
def gini(x,weights=None):
    if weights is None:
        weights = np.ones_like(x)
    # Calculate mean absolute deviation in two steps,for weights.
    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)
    # Gini equals half the relative mean absolute deviation.
    return 0.5 * rmad

这很干净,适用于中型阵列,但正如其最初的建议(https://stackoverflow.com/a/39513799/1840471)所警告的那样是O(n2).在我的计算机上,这意味着它在大约20k行之后中断：

n = 20000  # Works,30000 fails.
gini(np.random.rand(n),np.random.rand(n))

可以调整它以适用于更大的数据集吗？我的行是~150k行.

解决方法

def gini(x,w=None):
    # The rest of the code requires numpy arrays.
    x = np.asarray(x)
    if w is not None:
        w = np.asarray(w)
        sorted_indices = np.argsort(x)
        sorted_x = x[sorted_indices]
        sorted_w = w[sorted_indices]
        # Force float dtype to avoid overflows
        cumw = np.cumsum(sorted_w,dtype=float)
        cumxw = np.cumsum(sorted_x * sorted_w,dtype=float)
        return (np.sum(cumxw[1:] * cumw[:-1] - cumxw[:-1] * cumw[1:]) / 
                (cumxw[-1] * cumw[-1]))
    else:
        sorted_x = np.sort(x)
        n = len(x)
        cumx = np.cumsum(sorted_x,dtype=float)
        # The above formula,with all weights equal to 1 simplifies to:
        return (n + 1 - 2 * np.sum(cumx) / cumx[-1]) / n

这里有一些测试代码来检查我们得到(大多数)相同的结果：

>>> x = np.random.rand(1000000)
>>> w = np.random.rand(1000000)
>>> gini_slow(x,w)
0.33376310938610521
>>> gini(x,w)
0.33376310938610382

但速度差异很大：

%timeit gini(x,w)
203 ms ± 3.68 ms per loop (mean ± std. dev. of 7 runs,1 loop each)

%timeit gini_slow(x,w)
55.6 s ± 3.35 s per loop (mean ± std. dev. of 7 runs,1 loop each)

如果从函数中删除pandas ops,它已经快得多：

%timeit gini_slow2(x,w)
1.62 s ± 75 ms per loop (mean ± std. dev. of 7 runs,1 loop each)

如果你想获得最后一滴性能,你可以使用numba或cython,但这只会获得几个百分点,因为大部分时间都花在排序上.

%timeit ind = np.argsort(x); sx = x[ind]; sw = w[ind]
180 ms ± 4.82 ms per loop (mean ± std. dev. of 7 runs,10 loops each)

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