Which one of the following statements about the receiver operating characteristic (ROC) is FALSE?Group of answer choicesThe TPR is a non-decreasing function of the FPR, i.e. the ROC has a non-negative gradient everywhere. To obtain a smooth ROC, we typically need to average the ROC obtained in multiple rounds of cross-validation.The AUC (Area Under the Curve) is never equal to one under any circumstances.To plot the ROC in a (0,1) classification problem, we can use the "roc_curve" function as follows:from sklearn import metricsimport matplotlib.pyplot as pltfpr, tpr, threshold = metrics.roc_curve(y,scores)plt.plot(fpr,tpr)When FPR = 0, TPR must be 0. When FPR = 1, TPR must be 1.
Question
Which one of the following statements about the receiver operating characteristic (ROC) is FALSE?Group of answer choicesThe TPR is a non-decreasing function of the FPR, i.e. the ROC has a non-negative gradient everywhere. To obtain a smooth ROC, we typically need to average the ROC obtained in multiple rounds of cross-validation.The AUC (Area Under the Curve) is never equal to one under any circumstances.To plot the ROC in a (0,1) classification problem, we can use the "roc_curve" function as follows:from sklearn import metricsimport matplotlib.pyplot as pltfpr, tpr, threshold = metrics.roc_curve(y,scores)plt.plot(fpr,tpr)When FPR = 0, TPR must be 0. When FPR = 1, TPR must be 1.
Solution
The false statement is: "The AUC (Area Under the Curve) is never equal to one under any circumstances."
Explanation: The AUC (Area Under the Curve) can be equal to one. This happens when the model is able to perfectly distinguish between the positive and negative class. In other words, it has no false positives or false negatives, hence the AUC is 1. This is an ideal scenario and is rarely achieved in real-world scenarios.
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