What is the difference between precision recall and F1 score

Precision, recall, and F1 score are key metrics used to evaluate the performance of classification models, especially in cases where the classes are imbalanced. They provide different perspectives on how well a model is performing, focusing on different aspects of the classification results.

Precision

• Definition: Precision measures the proportion of true positive predictions (i.e., correctly identified positive cases) out of all positive predictions made by the model. It indicates how many of the predicted positive cases are actually positive.

• Formula: $\text{Precision} = \frac{\text{True Positives (TP)}}{\text{True Positives (TP)} + \text{False Positives (FP)}}$

• Usage: Precision is useful when the cost of false positives is high. For instance, in spam email detection, a high precision means fewer legitimate emails are incorrectly classified as spam.

• Interpretation: High precision means that when the model predicts a positive class, it is likely to be correct. Low precision indicates that there are many false positives.

• Example: If a model predicts 100 emails as spam, but only 80 of those are actually spam and 20 are legitimate emails, the precision is: $\text{Precision} = \frac{80}{100} = 0.8 \text{ or } 80\%$

Recall

• Definition: Recall (also known as Sensitivity or True Positive Rate) measures the proportion of actual positive cases that are correctly identified by the model. It indicates how many of the actual positive cases are captured by the model.

• Formula: $\text{Recall} = \frac{\text{True Positives (TP)}}{\text{True Positives (TP)} + \text{False Negatives (FN)}}$

• Usage: Recall is important when the cost of false negatives is high. For example, in medical diagnosis, high recall means that most patients with a disease are correctly identified, minimizing missed diagnoses.

• Interpretation: High recall means that the model captures most of the positive cases. Low recall indicates that many positive cases are missed.

• Example: If there are 100 actual spam emails and the model correctly identifies 80 of them as spam but misses 20, the recall is: $\text{Recall} = \frac{80}{100} = 0.8 \text{ or } 80\%$

F1 Score

• Definition: The F1 score is the harmonic mean of precision and recall. It provides a single metric that balances the trade-off between precision and recall, especially useful when you need a balance between the two.

• Formula: $\text{F1 Score} = 2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}}$

• Usage: The F1 score is useful when you need to balance precision and recall, and is particularly valuable in situations where both false positives and false negatives are important.

• Interpretation: The F1 score ranges from 0 to 1, with 1 being a perfect balance between precision and recall. Low F1 scores indicate that the model is not performing well in terms of either precision or recall.

• Example: Continuing with the previous precision and recall values (both 80%): $\text{F1 Score} = 2 \times \frac{0.8 \times 0.8}{0.8 + 0.8} = \frac{1.28}{1.6} = 0.8 \text{ or } 80\%$

Summary

• Precision focuses on the accuracy of positive predictions, i.e., how many of the predicted positives are actually positive. High precision means fewer false positives.
• Recall focuses on the ability to capture all positive cases, i.e., how many of the actual positives are captured. High recall means fewer false negatives.
• F1 Score combines precision and recall into a single metric, balancing the trade-off between them. It is useful when you need a single measure of performance that accounts for both false positives and false negatives.

In practice, the choice of which metric to prioritize depends on the specific problem and context of the classification task. For instance, in medical diagnosis, recall might be more critical to ensure that all potential cases are identified, while in fraud detection, precision might be prioritized to minimize false alarms.