Logistic regression is a statistical model that forces the output of an otherwise unbounded function to the interval (0,1).

$p(y=1 | x;\theta) = \sigma(\theta^\top x)$ $\sigma(x) = \frac{e^x}{e^x + 1}$ $p(y=0 | x;\theta) = 1 - p(y=1 | x;\theta)$

Where $\theta$ is the parameter vector.

For binary classification problems, logistic regression can be used instead of linear regression to handle the discontinuous nature of the target output.

However, the sigmoid function $\sigma$ has no local minimum or maximum, so a technique like gradient decent must be used instead.