Metrics for Evaluating Classifier Performance

Evaluating classifier performance involves various metrics, each providing insights into different aspects of the model's effectiveness:

1. Accuracy: The proportion of correctly classified instances out of the total instances. While simple, it can be misleading in imbalanced datasets. $$[ \text{Accuracy} = \frac{\text{True Positives} + \text{True Negatives}}{\text{Total Instances}} ]$$

2. Precision and Recall:

   • Precision: The ratio of true positive predictions to the total predicted positives. High precision indicates a low false positive rate. [ \text{Precision} = \frac{\text{True Positives}}{\text{True Positives} + \text{False Positives}} ]
   • Recall (Sensitivity): The ratio of true positive predictions to the total actual positives. High recall indicates a low false negative rate. [ \text{Recall} = \frac{\text{True Positives}}{\text{True Positives} + \text{False Negatives}} ]

3. F1-Score: The harmonic mean of precision and recall, providing a single metric that balances both concerns, especially useful in imbalanced datasets. $$[ \text{F1-Score} = 2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}} ]$$

4. Confusion Matrix: A matrix layout that allows visualization of the performance of an algorithm. It shows true positives, true negatives, false positives, and false negatives, providing a comprehensive view of the model's performance.

5. AUC-ROC (Area Under the Curve - Receiver Operating Characteristic): A plot of the true positive rate (recall) against the false positive rate. The area under this curve provides a single value summary of the classifier's ability to distinguish between classes. $$[ \text{AUC-ROC} = \int_0^1 \text{TPR} , d(\text{FPR}) ]$$