Receiver operating characteristics (ROC)

A ROC illustrates the diagnostic ability of a binary classifier as its discrimination threshold is varied. The ordinate in a ROC is the true positive rate (TPR) while the abscissa is the false positive rate (FPR). In real-world tasks, curves are usually drawn using a finite number of test samples {xi}i=1n, which yields a non-smooth appearance. In this case, we define the ROC as the piecewise linear curve formed by connecting points {(a1,b1),(a2,b2),,(am,bm)} in sequence(Note a1a2am, and b1b2bm ). - Let's consider a rank binary classifier. This classifier first computes a score for each sample by some function f(). Then, for some threshold , the classifier assigns Yi=1 for xi if f(xi)> while Yi=1 if f(xi)<. find a way to compute with classifier function f dataset and true labels let assume there are n samples nnegative we use d dto represent the sets of positive negative samples. loss l rank binary is defined as assuming that every sample has distinct score for i="j," show auc="1l," where area under roc curve>