202602251118
Status: #reference
Tags:
State: #nascient

(FBeta) E-Score

What if I want the F1-Score, but I want the ability to favor Precision (1-false discovery proportion) or Recall (Statistical Power).

Either because I am a lawyer or doctor who cares most about recall (cause missing a relevant document could mean jail/death for a customer/patient), but would still like some amount of precision to reduce my workload.

Or on the other hand, I am a greedy WIFI company trying to make sure I only detect people that are very likely to churn, but would still want to an extent to retrieve all the relevant people.

E-Score or $F\beta -$Score solves this by introducing a new tunable parameter $\beta$. It is computed as follows:

When $\beta =1$, this is exactly equal to the F1-Score.

When $\beta <1$, it favors Precision more.
When $\beta >1$, it favors Recall more.

To see why, it favors one rather than the other simply foil the expression. When $\beta >1$, recall is inflated by a factor of ${\beta }^2$ and when it's less than $1$ it's deflated by that same factor.

In practice, while any $\beta$ can be used, outside of $1$, $0.5$ and $2$ are the most commonly used according to this article: https://www.v7labs.com/blog/f1-score-guide

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