折损累积增益 (DCG) #

sklearn.metrics.dcg_score(y_true, y_score, *, k=None, log_base=2, sample_weight=None, ignore_ties=False)[source]#

计算折损累积增益。

应用对数折扣后，对由预测得分引起的顺序排列的真实得分进行求和。

如果真实标签由y_score排名靠前，则此排名指标会产生较高的值。

通常情况下，首选归一化折损累积增益 (NDCG，由ndcg_score计算)。

参数：

y_truearray-like of shape (n_samples, n_labels): 多标签分类的真实目标，或待排序实体的真实分数。
y_scorearray-like of shape (n_samples, n_labels): 目标分数，可以是概率估计、置信度值或非阈值决策度量（某些分类器返回的“decision_function”）。
kint, default=None: 仅考虑排名中最高的k个分数。如果为None，则使用所有输出。
log_basefloat, default=2: 用于折扣的对数底数。较低的值表示更尖锐的折扣（最高结果更重要）。
sample_weightarray-like of shape (n_samples,), default=None: 样本权重。如果为None，则所有样本都赋予相同的权重。
ignore_ties布尔值，默认值为False: 为提高效率，假设y_score中不存在任何平局（如果y_score是连续的，则很可能如此）。

返回:

discounted_cumulative_gain浮点数: 平均样本DCG分数。

另请参见

ndcg_score: 折扣累积增益除以理想折扣累积增益（完美排序获得的DCG），以便分数在0到1之间。

参考文献

维基百科词条：折扣累积增益.

Jarvelin, K., & Kekalainen, J. (2002). Cumulated gain-based evaluation of IR techniques. ACM Transactions on Information Systems (TOIS), 20(4), 422-446.

Wang, Y., Wang, L., Li, Y., He, D., Chen, W., & Liu, T. Y. (2013, May). A theoretical analysis of NDCG ranking measures. In Proceedings of the 26th Annual Conference on Learning Theory (COLT 2013).

McSherry, F., & Najork, M. (2008, March). Computing information retrieval performance measures efficiently in the presence of tied scores. In European conference on information retrieval (pp. 414-421). Springer, Berlin, Heidelberg.

示例

>>> import numpy as np
>>> from sklearn.metrics import dcg_score
>>> # we have ground-truth relevance of some answers to a query:
>>> true_relevance = np.asarray([[10, 0, 0, 1, 5]])
>>> # we predict scores for the answers
>>> scores = np.asarray([[.1, .2, .3, 4, 70]])
>>> dcg_score(true_relevance, scores)
np.float64(9.49...)
>>> # we can set k to truncate the sum; only top k answers contribute
>>> dcg_score(true_relevance, scores, k=2)
np.float64(5.63...)
>>> # now we have some ties in our prediction
>>> scores = np.asarray([[1, 0, 0, 0, 1]])
>>> # by default ties are averaged, so here we get the average true
>>> # relevance of our top predictions: (10 + 5) / 2 = 7.5
>>> dcg_score(true_relevance, scores, k=1)
np.float64(7.5)
>>> # we can choose to ignore ties for faster results, but only
>>> # if we know there aren't ties in our scores, otherwise we get
>>> # wrong results:
>>> dcg_score(true_relevance,
...           scores, k=1, ignore_ties=True)
np.float64(5.0)