What is the difference between accuracy, precision, recall, and F1-score?

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1. Accuracy

• The ratio of correctly predicted observations to the total observations.

• Formula:

  $$Accuracy = \frac{TP + TN}{TP + TN + FP + FN}$$

• It shows overall correctness but can be misleading in imbalanced datasets (e.g., when one class dominates).

2. Precision

• Out of all the instances the model predicted as positive, how many were actually positive.

• Formula:

  $$Precision = \frac{TP}{TP + FP}$$

• High precision means low false positive rate. Useful when the cost of false positives is high (e.g., spam detection, medical diagnosis).

3. Recall (Sensitivity / True Positive Rate)

• Out of all actual positive instances, how many were correctly predicted as positive.

• Formula:

  $$Recall = \frac{TP}{TP + FN}$$

• High recall means low false negative rate. Useful when the cost of false negatives is high (e.g., detecting cancer, fraud detection).

4. F1-Score

• The harmonic mean of precision and recall.

• Formula:

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

• Balances precision and recall, especially useful when classes are imbalanced.

• A high F1-score means the model achieves both good precision and recall.

In Simple Words

• Accuracy → Overall correctness.

• Precision → How many predicted positives are truly positive.

• Recall → How many actual positives are correctly identified.

• F1-score → Balance between precision and recall.

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