## Weighted Precision and Recall Equation

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”

## How to Compute the Derivative of a Sigmoid Function (fully worked example)

This is a sigmoid function:

$\boldsymbol{s(x) = \frac{1}{1 + e^{-x}}}$$\boldsymbol{s(x) = \frac{1}{1 + e^{-x}}}$

The sigmoid function looks like this (made with a bit of MATLAB code):

x=-10:0.1:10; s = 1./(1+exp(-x)); figure; plot(x,s); title('sigmoid');

Alright, now let’s put on our calculus hats…
Continue reading “How to Compute the Derivative of a Sigmoid Function (fully worked example)”