Exponential gain function in dcg calculation

[zkid18]

Describe the workflow you want to enable

Please correct me if I wrong.
Currently, the DCG score is calculated with the linear gain function.

    discount = 1 / (np.log(np.arange(y_true.shape[1]) + 2) / np.log(log_base))
    if k is not None:
        discount[k:] = 0
    if ignore_ties:
        ranking = np.argsort(y_score)[:, ::-1]
        ranked = y_true[np.arange(ranking.shape[0])[:, np.newaxis], ranking]
        cumulative_gains = discount.dot(ranked.T)
    else:
        discount_cumsum = np.cumsum(discount)
        cumulative_gains = [_tie_averaged_dcg(y_t, y_s, discount_cumsum)
                            for y_t, y_s in zip(y_true, y_score)]
        cumulative_gains = np.asarray(cumulative_gains)
    return cumulative_gains

However, in the industry, we use the alternative formulation of DCG as an exponential function, such as
gains = 2 ** y_true - 1
The exp function emphasis retrieving the highly relevant docs.

Can we add the alternative formulation of gain?

[zkid18]

A couple of references of dcg calculation with a dedicated interface for gain function selection:
https://gist.github.com/mblondel/7337391
https://github.com/catalyst-team/catalyst/blob/master/catalyst/metrics/ndcg.py (disclaimer: author of the patch)

[zkid18]

Reference for DCG calculation from cs276 Stanford slides
https://web.stanford.edu/class/cs276/handouts/EvaluationNew-handout-6-per.pdf

[jeromedockes]

I agree that as this transformation is very often used it could be useful to add a parameter that allows applying it. In the meanwhile IIUC it just amounts to providing different gains so this or any other transformation of the gains can be applied to y_true before passing it to ndcg_score: ndcg_score(2 ** y_true - 1, y_score) -- you can see the first parameter as "the true gains"

(detail: if a parameter is added to apply the exponential transformation, the implementation should check that the input gains are not too large)

[jeromedockes]

https://github.com/catalyst-team/catalyst/blob/master/catalyst/metrics/ndcg.py (disclaimer: author of the patch)

I think this link is outdated?