# Roc Auc Score

ROC AUC (Receiver Operating Characteristic - Area Under Curve) is a performance measurement for classification problems at various thresholds settings. It represents the degree or measure of separability.

Let's break it down a bit:

• ROC (Receiver Operating Characteristic) curve is a plot that illustrates the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings. The true positive rate is also known as recall or sensitivity, while the false positive rate is equal to 1-specificity. In other words, the ROC curve shows the trade-off between sensitivity (or recall) and specificity.
• AUC (Area Under The Curve) is literally just the area underneath the ROC curve. This metric tells us how much the model is capable of distinguishing between classes. The higher the AUC, the better the model is at distinguishing between positive and negative classes. If AUC is approximately 0.5, the model has no discrimination capacity and is generally considered to be performing no better than random guessing. If AUC is close to 1, then the model has excellent discrimination capacity.

The AUC ROC metric is very useful for binary classification problems, especially in cases where the classes in the dataset are not perfectly balanced. The ROC curve is also useful for comparing different models - the model with higher AUC can be considered the better model.

Remember, ROC AUC is a measure of how well a model can distinguish between different classes, it doesn't tell you about the exact values of false positives, true positives, etc. It also doesn't work well with imbalanced datasets. In such cases, you might want to use the Precision-Recall curve and its associated AUC.

Calculating the Receiver Operating Characteristic (ROC) curve and the Area Under the Curve (AUC) involves several steps:

1. Get the predicted probabilities: The ROC AUC score requires probabilities instead of predicted classes. For a binary classifier, this would be the predicted probability that each instance belongs to the positive class.
2. Sort instances by predicted probabilities: The instances are then sorted in descending order based on the predicted probabilities.
3. Calculate the True Positive Rate (TPR) and False Positive Rate (FPR): For each instance, starting with the one with the highest predicted probability, calculate the cumulative TPR (also known as recall or sensitivity) and FPR (1-specificity) as if the current instance is the last positive instance.

The TPR is calculated as follows:

TPR = True Positives / (True Positives + False Negatives)

The FPR is calculated as follows:

FPR = False Positives / (False Positives + True Negatives)

The True Positives, False Positives, etc. are calculated based on the current threshold (the predicted probability of the current instance). Everything above this threshold is classified as positive and everything below as negative.

1. Plot the ROC curve: The ROC curve is then created by plotting the cumulative FPR on the X-axis and the cumulative TPR on the Y-axis.
2. Calculate the AUC: The AUC is the area under the ROC curve. This can be approximated by using the trapezoidal rule, which calculates the area under a curve by breaking it up into a series of trapezoids. The sum of the areas of these trapezoids gives the total area under the curve.