dask / dask/dask-ml

Area under the receiving operating characteristic curve (AUROC) calculation.

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Description

A common metric for classification model performance is the area under the receiving operating characteristic curve (AUROC, AUROCC, or often simply AUC) which shows the area of the curve created by plotting TPR and FPR against one another.
[Wikipedia](https://en.wikipedia.org/wiki/Receiver_operating_characteristic).

This metric [is available in sklearn](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.roc_auc_score.html), but is currently missing from Dask-ml. One issue with computing this metric in Dask is that the standard implementation of AUROC requires searching over a sorted array and the sorting operations are often expensive in distributed computing.

I would be interested in a discussion of whether a naive version of this could be implemented using sorting and whether there are any known methods of computation that avoid the sort.

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