What are precision and recall

Precision and recall are two fundamental metrics used to evaluate the performance of a classification model, especially in the context of binary classification. They are particularly useful when dealing with imbalanced datasets, where the number of instances in each class is significantly different.

Precision

Precision is the ratio of correctly predicted positive observations to the total predicted positives. It answers the question: "Of all the instances that were predicted as positive, how many were actually positive?"

Precision=True Positives (TP)True Positives (TP)+False Positives (FP)\text{Precision} = \frac{\text{True Positives (TP)}}{\text{True Positives (TP)} + \text{False Positives (FP)}}Precision=True Positives (TP)+False Positives (FP)True Positives (TP)?

• True Positives (TP): The number of positive instances correctly predicted by the model.
• False Positives (FP): The number of negative instances incorrectly predicted as positive by the model.

High precision indicates a low false positive rate.

Recall (Sensitivity or True Positive Rate)

Recall is the ratio of correctly predicted positive observations to all the observations in the actual class. It answers the question: "Of all the instances that were actually positive, how many were predicted as positive?"

Recall=True Positives (TP)True Positives (TP)+False Negatives (FN)\text{Recall} = \frac{\text{True Positives (TP)}}{\text{True Positives (TP)} + \text{False Negatives (FN)}}Recall=True Positives (TP)+False Negatives (FN)True Positives (TP)?

• False Negatives (FN): The number of positive instances incorrectly predicted as negative by the model.

High recall indicates a low false negative rate.

Example

Consider a binary classification problem where we want to identify whether an email is spam (positive class) or not spam (negative class).

• True Positives (TP): Emails correctly classified as spam.
• False Positives (FP): Emails incorrectly classified as spam (actually not spam).
• True Negatives (TN): Emails correctly classified as not spam.
• False Negatives (FN): Emails incorrectly classified as not spam (actually spam).

Suppose we have the following confusion matrix:

From this confusion matrix:

• Precision = 5050+5=5055≈0.91\frac{50}{50 + 5} = \frac{50}{55} \approx 0.9150+550?=5550?≈0.91
• Recall = 5050+10=5060≈0.83\frac{50}{50 + 10} = \frac{50}{60} \approx 0.8350+1050?=6050?≈0.83

Balancing Precision and Recall

In many applications, there is a trade-off between precision and recall. Improving precision typically reduces recall and vice versa. The choice between optimizing precision or recall depends on the specific context of the problem:

• High Precision, Lower Recall: Useful when the cost of false positives is high. For example, in email spam detection, we prefer high precision to avoid misclassifying important emails as spam.
• High Recall, Lower Precision: Useful when the cost of false negatives is high. For example, in medical diagnosis, we prefer high recall to ensure that most actual positive cases (e.g., disease cases) are detected.

F1 Score

The F1 score is the harmonic mean of precision and recall, providing a single metric that balances both concerns. It is particularly useful when you need to find an optimal balance between precision and recall.

F1 Score=2×Precision×RecallPrecision+Recall\text{F1 Score} = 2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}}F1 Score=2×Precision+RecallPrecision×Recall?

In the example above:

F1 Score=2×0.91×0.830.91+0.83≈0.87\text{F1 Score} = 2 \times \frac{0.91 \times 0.83}{0.91 + 0.83} \approx 0.87F1 Score=2×0.91+0.830.91×0.83?≈0.87

Conclusion

Precision and recall are essential metrics for evaluating the performance of classification models, especially in scenarios with imbalanced datasets. Understanding and balancing these metrics is crucial for developing effective and reliable models tailored to the specific needs of an application.