Area Under the ROC Curve (AUC) is a metric that is best suited to score the model for the given scenario. AUC is a measure of the performance of a binary classifier, such as a model that predicts whether a credit card transaction is valid or fraudulent. AUC is calculated based on the Receiver Operating Characteristic (ROC) curve, which is a plot that shows the trade-off between the true positive rate (TPR) and the false positive rate (FPR) of the classifier as the decision threshold is varied. The TPR, also known as recall or sensitivity, is the proportion of actual positive cases (fraudulent transactions) that are correctly predicted as positive by the classifier. The FPR, also known as the fall-out, is the proportion of actual negative cases (valid transactions) that are incorrectly predicted as positive by the classifier. The ROC curve illustrates how well the classifier can distinguish between the two classes, regardless of the class distribution or the error costs. A perfect classifier would have a TPR of 1 and an FPR of 0 for all thresholds, resulting in a ROC curve that goes from the bottom left to the top left and then to the top right of the plot. A random classifier would have a TPR and an FPR that are equal for all thresholds, resulting in a ROC curve that goes from the bottom left to the top right of the plot along the diagonal line. AUC is the area under the ROC curve, and it ranges from 0 to 1. A higher AUC indicates a better classifier, as it means that the classifier has a higher TPR and a lower FPR for all thresholds. AUC is a useful metric for imbalanced classification problems, such as the credit card transaction dataset, because it is insensitive to the class imbalance and the error costs. AUC can capture the overall performance of the classifier across all possible scenarios, and it can be used to compare different classifiers based on their ROC curves.

The other options are not as suitable as AUC for the given scenario for the following reasons:

Precision: Precision is the proportion of predicted positive cases (fraudulent transactions) that are actually positive. Precision is a useful metric when the cost of a false positive is high, such as in spam detection or medical diagnosis. However, precision is not a good metric for imbalanced classification problems, because it can be misleadingly high when the positive class is rare. For example, a classifier that predicts all transactions as valid would have a precision of 0, but a very high accuracy of 99%. Precision is also dependent on the decision threshold and the error costs, which may vary for different scenarios.

Recall: Recall is the same as the TPR, and it is the proportion of actual positive cases (fraudulent transactions) that are correctly predicted as positive by the classifier. Recall is a useful metric when the cost of a false negative is high, such as in fraud detection or cancer diagnosis. However, recall is not a good metric for imbalanced classification problems, because it can be misleadingly low when the positive class is rare. For example, a classifier that predicts all transactions as fraudulent would have a recall of 1, but a very low accuracy of 1%. Recall is also dependent on the decision threshold and the error costs, which may vary for different scenarios.

Root Mean Square Error (RMSE): RMSE is a metric that measures the average difference between the predicted and the actual values. RMSE is a useful metric for regression problems, where the goal is to predict a continuous value, such as the price of a house or the temperature of a city. However, RMSE is not a good metric for classification problems, where the goal is to predict a discrete value, such as the class label of a transaction. RMSE is not meaningful for classification problems, because it does not capture the accuracy or the error costs of the predictions.

ROC Curve and AUC

How and When to Use ROC Curves and Precision-Recall Curves for Classification in Python

Precision-Recall

Root Mean Squared Error