F1 Score

machine-learning

Definition

F1 Score

The F1 scores tries to sum up the insights from the precision and recall metric into one.

$$\begin{array}{rl}\text{F1}& =\frac{2}{\frac{1}{\text{Precision}}+\frac{1}{\text{Recall}}}\\ & =\frac{2\cdot \text{TPR}\cdot \text{PPV}}{\text{TPR}+\text{PPV}}\\ & =\frac{\left(2\cdot \frac{\text{TP}}{\text{TP}+\text{FN}}\cdot \frac{\text{TP}}{\text{TP}+\text{FP}}\right)}{\frac{\text{TP}}{\text{TP}+\text{FN}}+\frac{\text{TP}}{\text{TP}+\text{FP}}}\\ & =\frac{2\cdot \text{TP}}{2\cdot \text{TP}+\text{FP}+\text{FN}}\end{array}$$

where:

• $\text{TPR}$: True Positive Rate
• $\text{PPV}$: Positive Predictive Value
• $\text{TP}$: True Positive
• $\text{FP}$: False Positive
• $\text{FN}$: False Negative