The sigmoid is a function with an s shape that's used in logistic regression (and
elsewhere).


The Equation



\[\begin{aligned}
\sigma(z) &= \frac{1}{1+e^{-z}}\\
\sigma(0) &= \frac{1}{2}\\
 \lim_{z \to \infty} \sigma(z) &= 1\\
 \lim_{z \to -\infty} \sigma(z) &= 0\\
 \end{aligned}\]

Applying to a Linear Regression Classifier

  1. Apply the Sigmoid to z multiplied by a weight learned by the classifier.
  2. Classify using round(Sigmoid(z))