dcg_score(y_true, y_score, k=None, log_base=2, sample_weight=None, ignore_ties=False)¶
Compute Discounted Cumulative Gain.
Sum the true scores ranked in the order induced by the predicted scores, after applying a logarithmic discount.
This ranking metric yields a high value if true labels are ranked high by
Usually the Normalized Discounted Cumulative Gain (NDCG, computed by ndcg_score) is preferred.
- y_truendarray, shape (n_samples, n_labels)
True targets of multilabel classification, or true scores of entities to be ranked.
- y_scorendarray, shape (n_samples, n_labels)
Target scores, can either be probability estimates, confidence values, or non-thresholded measure of decisions (as returned by “decision_function” on some classifiers).
- kint, optional (default=None)
Only consider the highest k scores in the ranking. If None, use all outputs.
- log_basefloat, optional (default=2)
Base of the logarithm used for the discount. A low value means a sharper discount (top results are more important).
- sample_weightndarray, shape (n_samples,), optional (default=None)
Sample weights. If None, all samples are given the same weight.
- ignore_tiesbool, optional (default=False)
Assume that there are no ties in y_score (which is likely to be the case if y_score is continuous) for efficiency gains.
The averaged sample DCG scores.
The Discounted Cumulative Gain divided by the Ideal Discounted Cumulative Gain (the DCG obtained for a perfect ranking), in order to have a score between 0 and 1.
- `Wikipedia entry for Discounted Cumulative Gain
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.
>>> from sklearn.metrics import dcg_score >>> # we have groud-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) # doctest: +ELLIPSIS 9.49... >>> # we can set k to truncate the sum; only top k answers contribute >>> dcg_score(true_relevance, scores, k=2) # doctest: +ELLIPSIS 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) # doctest: +ELLIPSIS 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) # doctest: +ELLIPSIS 5.0