auc-roc-loss-function

A TensorFlow loss function for binary classification based on an approximation of the normalized Wilcoxon-Mann-Whitney (WMW) statistic.

The normalized WMW statistic can be shown to be equal to the AUC-ROC. However, it is a step function so it is not differentiable. The normalized WCW statistic can be approximated with a smooth, differentiable function which makes the approximated version a near ideal loss function for optimizing for the AUC-ROC metric.

The loss function has two parameters, gamma and p, which are recommended to be kept between 0.1 to 0.7 and at 2 or 3, respectively.

Example use of loss function.

For more information: Optimizing Classifier Performance via an Approximation to the Wilcoxon-Mann-Whitney Statistic. Yan, Lian and Dodier, Robert H. and Mozer, Michael and Wolniewicz, Richard H. International Conference on Machine Learning (2003).