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 computerecall, 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”