The **“weighted”** precision or recall score using `sciki-learn`

is defined as,

$$

\frac{1}{\sum_{l\in \color{cyan}{L}} |\color{green}{\hat{y}}_l|}

\sum_{l \in \color{cyan}{L}}

|\color{green}{\hat{y}}_l|

\phi(\color{magenta}{y}_l, \color{green}{\hat{y}}_l)

$$

- \(\color{cyan}{L}\) is the set of labels
- \(\color{green}{\hat{y}}\) is the true label
- \(\color{magenta}{y}\) is the predicted label
- \(\color{green}{\hat{y}}_l\) is all the true labels that have the label \(l\)
- \(|\color{green}{\hat{y}}_l|\) is the number of true labels that have the label \(l\)
- \(\phi(\color{magenta}{y}_l, \color{green}{\hat{y}}_l)\) computes the precision or recall for the true and predicted labels that have the label \(l\). To compute
`precision`

, let \(\phi(A,B) = \frac{|A \cap B|}{|A|}\). To compute`recall`

, let \(\phi(A,B) = \frac{|A \cap B|}{|B|}\).

## How is Weighted Precision and Recall Calculated?

Let’s break this apart a bit more.

Continue reading “Weighted Precision and Recall Equation”