Gini系數的原理

轉載：https://blog.csdn.net/u010665216/article/details/78528261

首先，我們直接構造賽題結果：真實數據與預測數據：

predictions = [0.9, 0.3, 0.8, 0.75, 0.65, 0.6, 0.78, 0.7, 0.05, 0.4, 0.4, 0.05, 0.5, 0.1, 0.1]
actual = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]

我們將預測值從小到大排列：

data = zip(actual, predictions)
sorted_data = sorted(data, key=lambda d: d[1])
sorted_actual = [d[0] for d in sorted_data]
print('Sorted Actual Values', sorted_actual)

我們對排序后的真實值累計求和：

cumulative_actual = np.cumsum(sorted_actual)
cumulative_index = np.arange(1, len(cumulative_actual)+1)

plt.plot(cumulative_index, cumulative_actual)
plt.xlabel('Cumulative Number of Predictions')
plt.ylabel('Cumulative Actual Values')
plt.show()

我們將數據Normalization到0，1之間，並畫出45度線：

cumulative_actual_shares = cumulative_actual / sum(actual)
cumulative_index_shares = cumulative_index / len(predictions)

#Add (0, 0) to the plot
x_values = [0] + list(cumulative_index_shares)
y_values = [0] + list(cumulative_actual_shares)

#Display the 45° line stacked on top of the y values
diagonal = [x - y for (x, y) in zip(x_values, y_values)]

plt.stackplot(x_values, y_values, diagonal)
plt.xlabel('Cumulative Share of Predictions')
plt.ylabel('Cumulative Share of Actual Values')
plt.show()

計算橙色區域面積：

fy = scipy.interpolate.interp1d(x_values, y_values)
blue_area, _ = scipy.integrate.quad(fy, 0, 1, points=x_values)
orange_area = 0.5 - blue_area
print('Orange Area: %.3f' % orange_area)

最大可能的基尼系數：

前面我們是按照預測值對真實值排序，得到一個基尼系數；現在我們按照真實值給真實值排序，得到最大可能的基尼系數：

cumulative_actual_shares_perfect = np.cumsum(sorted(actual)) / sum(actual)
y_values_perfect = [0] + list(cumulative_actual_shares_perfect)

#Display the 45° line stacked on top of the y values
diagonal = [x - y for (x, y) in zip(x_values, y_values_perfect)]

plt.stackplot(x_values, y_values_perfect, diagonal)
plt.xlabel('Cumulative Share of Predictions')
plt.ylabel('Cumulative Share of Actual Values')
plt.show()

# Integrate the the curve function
fy = scipy.interpolate.interp1d(x_values, y_values_perfect)
blue_area, _ = scipy.integrate.quad(fy, 0, 1, points=x_values)
orange_area = 0.5 - blue_area
print('Orange Area: %.3f' % orange_area)

數據挖掘中的Scoring Metric的實現：

def gini(actual, pred):
    assert (len(actual) == len(pred))
    all = np.asarray(np.c_[actual, pred, np.arange(len(actual))], dtype=np.float)
    all = all[np.lexsort((all[:, 2], -1 * all[:, 1]))]
    totalLosses = all[:, 0].sum()
    giniSum = all[:, 0].cumsum().sum() / totalLosses

    giniSum -= (len(actual) + 1) / 2.
    return giniSum / len(actual)


def gini_normalized(actual, pred):
    return gini(actual, pred) / gini(actual, actual)


gini_predictions = gini(actual, predictions)
gini_max = gini(actual, actual)
ngini= gini_normalized(actual, predictions)
print('Gini: %.3f, Max. Gini: %.3f, Normalized Gini: %.3f' % (gini_predictions, gini_max, ngini))