Summary  
This chapter explains how to calculate and interpret the F1 score—the harmonic mean of precision and recall—as a balanced evaluation metric for classification models.  

General domain of usage  
Evaluation of classification models in machine learning, especially on imbalanced datasets.

The **F1 score** is a crucial metric for evaluating classification models, especially when dealing with imbalanced datasets. Unlike **accuracy**, which simply measures the proportion of correct predictions, the F1 score combines both **precision** and **recall** into a single value. 

- **Precision** measures how many of the predicted positive instances are truly positive;
- **Recall** measures how many of the actual positive instances were correctly identified.

The F1 score is defined as the **harmonic mean** of precision and recall. The harmonic mean gives more weight to lower values, ensuring that both precision and recall must be high for a good F1 score. The formula for the F1 score is:

$$
F1 = 2 \times \frac{\text{precision} \times \text{recall}}{\text{precision} + \text{recall}}
$$

This formula highlights that the F1 score will only be high if both precision and recall are high. If either is low, the F1 score will decrease significantly, making it a balanced metric for situations where you need to consider both false positives and false negatives.

from sklearn.metrics import f1_score

# Simulated true labels and predicted labels for a classification task
y_true = [1, 0, 1, 1, 0, 1, 0, 0, 1, 0]
y_pred = [1, 0, 1, 0, 0, 1, 1, 0, 0, 0]

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

print(f"F1 Score: {f1:.2f}")

The **F1 score** ranges from `0` (worst) to `1` (best), reflecting the balance between **precision** and **recall**. A score of `1` means your model achieves both perfect precision and recall, while a score near `0` indicates poor performance on both fronts.

Use the F1 score to:
- Evaluate models where both false positives and false negatives carry significant consequences;
- Assess performance on **imbalanced datasets**, where one class is much more common than the other;
- Summarize model effectiveness with a single value that penalizes extreme trade-offs between precision and recall.

Prefer the F1 score over accuracy when:
- The dataset contains a strong class imbalance;
- Both types of error (false positives and false negatives) are costly;
- You need a metric that discourages optimizing for only precision or only recall.

Rely on the F1 score when you need a comprehensive view of your model's ability to correctly identify positive cases without producing too many false alarms.

Which statement best describes the F1 score and when it is most useful in classification tasks

A comprehensive course for intermediate learners to master the key evaluation metrics used in machine learning, covering both supervised and unsupervised tasks. The course progresses from foundational concepts to practical Python implementations, interpretation of results, and a comparative overview of metric types and their trade-offs.

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