The ROC (Receiver Operating Characteristic) curve is a graphical representation used to evaluate the performance of a binary classification model. It can only be used with classifiers that return a score (or a probability) of prediction.
- True Positive Rate (TPR) or Sensitivity (Y-axis): This is the proportion of actual positive cases that are correctly identified by the model. It is calculated as:
- False Positive Rate (FPR) (X-axis): This is the proportion of actual negative cases that are incorrectly identified as positive by the model. It is calculated as:
#Interpretation
- ROC Curve Shape: The ROC curve plots the TPR against the FPR at various threshold settings. A model that performs perfectly would have a ROC curve that passes through the top-left corner (TPR = 1, FPR = 0). A model that performs no better than random chance would have a ROC curve that is a diagonal line from the bottom-left to the top-right (TPR = FPR).
- Area Under the Curve (AUC-ROC): The AUC-ROC is a single scalar value that summarizes the performance of the model. It represents the probability that a randomly chosen positive instance is ranked higher than a randomly chosen negative instance. An AUC of 1 indicates perfect performance, while an AUC of 0.5 indicates performance no better than random chance.
#Example
Imagine you have a binary classifier for detecting spam emails:
- True Positives (TP): Emails correctly identified as spam.
- False Positives (FP): Emails incorrectly identified as spam (but are actually not spam).
- True Negatives (TN): Emails correctly identified as not spam.
- False Negatives (FN): Emails incorrectly identified as not spam (but are actually spam). The ROC curve helps visualize the trade-off between the TPR and FPR at different threshold levels, providing a comprehensive view of the model’s performance across all possible classification thresholds.
Recall