What are precision, recall, and F1-score?

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Precision, recall, and F1-score are evaluation metrics used in classification problems, especially when dealing with imbalanced datasets.

1. Precision

Precision measures how many of the positive predictions made by the model are actually correct.

$$\text{Precision} = \frac{True\ Positives}{True\ Positives + False\ Positives}$$

High precision means that when the model predicts something as positive, it’s usually correct. It's useful when the cost of false positives is high (e.g., spam detection).

2. Recall

Recall (also called sensitivity) measures how many of the actual positive cases the model correctly identified.

$$\text{Recall} = \frac{True\ Positives}{True\ Positives + False\ Negatives}$$

High recall means the model is good at finding all the positive cases. It's important when missing positives is costly (e.g., disease diagnosis).

3. F1-score

The F1-score is the harmonic mean of precision and recall, providing a balance between the two.

$$\text{F1-score} = 2 \times \frac{Precision \times Recall}{Precision + Recall}$$

It’s especially useful when you need a single measure that balances both precision and recall.

Example:

• A model predicts 100 emails as spam.

• 80 are truly spam (true positives), 20 are not (false positives).

• There were 100 actual spam emails, but the model only found 80 of them (20 false negatives).

• Precision = 80 / (80 + 20) = 0.80

• Recall = 80 / (80 + 20) = 0.80

• F1-score = 2 × (0.8 × 0.8) / (0.8 + 0.8) = 0.80

These metrics help evaluate model performance beyond simple accuracy.

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