What are precision, recall, and F1-score?

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

1. Precision measures how many of the predicted positive results are actually correct. It’s calculated as:

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

   High precision means that the model returns more relevant results than irrelevant ones.

2. Recall (also known as sensitivity or true positive rate) measures how many actual positive cases the model correctly identified. It’s given by:

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

   High recall indicates that the model captures most of the relevant cases, even if it includes some incorrect predictions.

3. F1-score is the harmonic mean of precision and recall. It balances the two by penalizing extreme values, especially when one is much lower than the other:

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

   F1 is useful when both false positives and false negatives are important, and when there's a need to balance precision and recall.

These metrics are especially important in fields like medical diagnosis, fraud detection, or spam filtering, where simply measuring accuracy might be misleading due to class imbalance.

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