AUC-ROC Curve

The AUC-ROC curve, often referred to as the ROC curve, is a graphical representation of the performance of a binary classification model. ROC stands for Receiver Operating Characteristic, and AUC stands for Area Under the Curve. The ROC curve plots the true positive rate (Sensitivity) against the false positive rate (1 – Specificity) at various classification thresholds, and the AUC represents the overall performance of the model.

Here’s how the AUC-ROC curve is constructed and interpreted:

Model prediction: The binary classification model assigns a probability or a score to each instance, indicating the likelihood of belonging to the positive class. These scores are used to rank the instances.

Threshold selection: Starting from the highest score, a threshold is progressively decreased. Instances with scores above the threshold are classified as positive, while those below the threshold are classified as negative.

True Positive Rate (Sensitivity): At each threshold, the true positive rate (TPR) is calculated as the proportion of actual positive instances that are correctly classified as positive. It is also known as sensitivity, recall, or the hit rate.

False Positive Rate (1 – Specificity): At each threshold, the false positive rate (FPR) is calculated as the proportion of actual negative instances that are incorrectly classified as positive. It is equal to (1 – Specificity) and represents the fraction of negative instances that are falsely classified as positive.

Plotting the curve: The ROC curve is constructed by plotting the TPR against the FPR for different threshold values. Each point on the curve represents a specific trade-off between the true positive rate and the false positive rate.

Interpretation: The ROC curve provides a visual representation of the model’s performance across different classification thresholds. A model with better performance will have a curve that is closer to the top-left corner of the plot, indicating higher TPR and lower FPR values. The AUC summarizes the overall performance of the model by calculating the area under the ROC curve. The AUC ranges from 0 to 1, where a higher AUC indicates better classification performance. An AUC of 0.5 represents a random classifier, while an AUC of 1 represents a perfect classifier.

The AUC-ROC curve is commonly used to evaluate and compare the performance of binary classification models, especially when the class distribution is imbalanced. It provides insights into the trade-off between sensitivity and specificity and helps in choosing an appropriate classification threshold based on the desired balance between true positives and false positives.