Optimising area under the ROC curve using gradient descent

This paper introduces RankOpt, a linear binary classifier which optimises the area under the ROC curve (the AUC). Unlike standard binary classifiers, RankOpt adopts the AUC statistic as its objective function, and optimises it directly using gradient descent. The problems with using the AUC statistic as an objective function are that it is non-differentiable, and of complexity O(n2) in the number of data observations. RankOpt uses a differentiable approximation to the AUC which is accurate, and computationally efficient, being of complexity O(n.) This enables the gradient descent to be performed in reasonable time. The performance of RankOpt is compared with a number of other linear binary classifiers, over a number of different classification problems. In almost all cases it is found that the performance of RankOpt is significantly better than the other classifiers tested.