View source for F1 Score

= F1 Score =

The '''F1 Score''' is a performance metric used in classification problems that balances the trade-off between [[Precision]] and [[Recall]] (also known as [[Sensitivity]]). It is especially useful when the dataset is imbalanced, and both false positives and false negatives are important.

== Definition ==

The F1 Score is the '''harmonic mean''' of Precision and Recall.

:<math> F1 = 2 \cdot \frac{\text{Precision} \cdot \text{Recall}}{\text{Precision} + \text{Recall}} </math>

Where:
* '''Precision''' = <math> \frac{TP}{TP + FP} </math>
* '''Recall''' = <math> \frac{TP}{TP + FN} </math>
* '''TP''' = True Positives
* '''FP''' = False Positives
* '''FN''' = False Negatives

== Why Harmonic Mean? ==

The harmonic mean punishes extreme values more than the arithmetic mean. So if either precision or recall is very low, the F1 score will be low too. This makes it a balanced measure when you need both high precision and recall.

== Simple Example ==

Imagine a medical test for a disease:

* True Positives (TP) = 80  
* False Positives (FP) = 20  
* False Negatives (FN) = 10  

First, calculate:

:<math> \text{Precision} = \frac{80}{80 + 20} = 0.8 </math>  
:<math> \text{Recall} = \frac{80}{80 + 10} = 0.8889 </math>  

Now compute F1 Score:

:<math> F1 = 2 \cdot \frac{0.8 \cdot 0.8889}{0.8 + 0.8889} \approx 2 \cdot \frac{0.7111}{1.6889} \approx 0.841 </math>

== When to Use F1 Score ==

Use the F1 Score when:
* You care equally about false positives and false negatives
* The dataset is imbalanced
* Neither precision nor recall alone gives a complete picture

== Not Ideal When ==

* Class distribution is balanced and you want to evaluate overall correctness → [[Accuracy]] may be enough.
* You want to analyze performance per class → Consider using [[Macro F1]] or [[Weighted F1]] in multi-class problems.

== F1 Score Variants ==

* '''Micro F1''': Aggregates total TP, FP, FN across all classes before computing F1
* '''Macro F1''': Calculates F1 for each class, then averages
* '''Weighted F1''': Like macro, but weighted by class support (number of instances)

== Related Metrics ==

* [[Precision]]
* [[Recall]]
* [[Accuracy]]
* [[Confusion Matrix]]
* [[Specificity]]
* [[ROC Curve]]

== SEO Keywords ==

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[[Category:Artificial Intelligence]]