F1 score

The F1 score is a commonly used metric for evaluating the performance of classification models. It considers both precision and recall to provide a single score that balances between them. The F1 score is the harmonic mean of precision and recall and is calculated using the following formula:

$F_1 = 2 \times \frac{{\text{{precision}} \times \text{{recall}}}}{{\text{{precision}} + \text{{recall}}}}$

where:

• Precision is the ratio of true positive predictions to the total number of positive predictions, indicating the accuracy of positive predictions among all predicted positives.

• Recall (also known as sensitivity) is the ratio of true positive predictions to the total number of actual positives, indicating the proportion of actual positives that were correctly identified.

Interpretation:

• The F1 score ranges from 0 to 1, where a higher score indicates better model performance.

• A perfect F1 score of 1 means perfect precision and recall, indicating that all positive predictions are correct, and all actual positives are correctly identified.

• A lower F1 score indicates that either precision or recall (or both) is low, suggesting that the model's performance needs improvement.

• The F1 score provides a balance between precision and recall, making it useful when there is an uneven class distribution or when both false positives and false negatives are equally important.

Python Implementation (using scikit-learn):

from sklearn.metrics import f1_score

# Example ground truth and predicted labels
y_true = [0, 1, 1, 0, 1]
y_pred = [0, 1, 0, 0, 1]

# Calculate F1 score
f1 = f1_score(y_true, y_pred)

print("F1 Score:", f1)

In this example, y_true contains the true labels of the samples, and y_pred contains the predicted labels. We calculate the F1 score using the f1_score function from scikit-learn's metrics module.