F-Beta Score

#evaluation #machine-learning #interview

F_{β}

Score

$\begin{aligned} F_{β} & = (1 + β^{2}) \frac{P r e c i s i o n * R e c a l l}{β^{2} * P r e c i s i o n + R e c a l l} \\ = \frac{(1 + β^{2}) * T P}{(1 + β^{2}) * T P + β^{2} * F N + F P} \end{aligned}$

If precision and recall is equally important, then use $β$ = 1 which becomes F1 Score
If False positive has more importance, then use $β$ = $[0, 1]$
- as that will make FN weight less on denominator and so FN weight more overall
- So if FN is big -> $β * F N$ will be small -> the $F_{β}$ will be big
- But if FP is big -> the $F_{β}$ will be small
If False Negative has more importance, the use $β$ > 1
- As that will make FN weight more on denominator and so FN weight less overall
- So if FN is big -> $β * F N$ will be bigger -> the $F_{β}$ will be small
- But it FP is big -> the weight is smaller than $β * F N$ , so has less weight on $F_{β}$

References

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