Calculating the F2 score using Python's sklearn

The F2 score is a specialized metric in machine learning designed to evaluate the performance of classification models. It is particularly significant in scenarios where false negatives are more costly than false positives. For instance, missing a positive case can have severe consequences in medical diagnosis or fraud detection compared to a false alarm. This metric is important for balancing precision and recall, with a higher emphasis on recall.

Precision and recall: the building blocks

• Precision measures the accuracy of positive predictions made by a model. It is calculated as the number of true positives divided by the sum of true positives and false positives.
• Recall, on the other hand, measures how well a model identifies all relevant instances. It is calculated as the number of true positives divided by the sum of true positives and false negatives.

The F2 score formula and calculation

The F2 score is calculated using the formula:

[ F_2 = \frac{(1 + 2^2) \times \text{Precision} \times \text{Recall}}{2^2 \times \text{Precision} + \text{Recall}} ]

This formula emphasizes recall over precision, making it suitable for applications where missing a positive instance is detrimental.

Implementation in Python

Python's sklearn library simplifies the calculation of the F2 score. However, since sklearn does not directly support the F2 score, you can calculate it manually using the formula above or use custom functions to achieve similar results.

def calculate_f2_score(precision, recall):     return ((1 + 2**2) * precision * recall) / (2**2 * precision + recall)

# Example usage precision = 0.8  # Example precision value recall = 0.9     # Example recall value

f2_score = calculate_f2_score(precision, recall) print("F2 Score:", f2_score)

Applications of the F2 score

Medical diagnosis

The F2 score is invaluable for detecting diseases early in medical diagnosis. Missing a positive diagnosis (false negative) can have more severe consequences than a false alarm (false positive). For instance, a study might use the F2 score to evaluate the performance of a model designed to diagnose rare diseases.

Fraud detection

In banking and finance, the F2 score helps detect fraudulent transactions. Failing to identify fraud can lead to significant financial losses, making recall a priority over precision. A high F2 score would effectively minimize false negatives in this context.

Customer churn prediction

When predicting customer churn, the F2 score can be used to ensure that all potential churners are identified. Missing a customer who might churn (false negative) is more costly than mistakenly flagging a non-churner (false positive).

Comparison with other metrics

There are other types of metrics to consider:

Accuracy

Accuracy measures the proportion of true results among all cases but can be misleading in imbalanced datasets. For instance, in a scenario where only 1% of the data is positive, a model predicting all negatives would have 99% accuracy but fail to identify any true positives.

F1 score

The F1 score gives equal weight to precision and recall, making it less suitable for scenarios where false negatives are more critical. It is calculated as:

[ F_1 = 2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}} ]

ROC-AUC

The ROC-AUC (area under the receiver operating characteristic curve) measures the model's ability to distinguish between classes. It is useful when the cost of false positives and false negatives varies, but it does not directly emphasize recall or precision like the F2 score.

When to use the F2 score

The F2 score is an essential metric in machine learning, particularly in scenarios where the cost of false negatives is high. By emphasizing recall over precision, it ensures that models are evaluated based on their ability to identify all relevant instances, even if it means allowing some false positives.

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Sources cited

• Deepgram. "F2 Score." Deepgram AI Glossary, https://deepgram.com/ai-glossary/f2-score.
• Giskard. "F Score." Giskard AI Glossary, https://www.giskard.ai/glossary/f-score.
• H2O.ai. "Scorers." H2O.ai Driverless AI Documentation, https://docs.h2o.ai/driverless-ai/latest-stable/docs/userguide/scorers.html.
• Machine Learning Mastery. "The Fbeta Measure for Machine Learning." Machine Learning Mastery, https://machinelearningmastery.com/fbeta-measure-for-machine-learning/.
• Scikit-learn. "Model evaluation: Quantifying the quality of predictions." Scikit-learn Documentation, https://scikit-learn.org/stable/modules/model_evaluation.html.
• V7 Labs. "The F1 Score Guide: Precision, Recall, and When to Use Each." V7 Labs, https://www.v7labs.com/blog/f1-score-guide.