Logistic regression for classification

In the previous section, we learned how to predict. There's another common task in ML: the task of classification. Separating dogs from cats and spam from not spam, or even identifying the different objects in a room or scene—all of these are classification tasks. 

Logistic regression is an old classification technique. It provides the probability of an event taking place, given an input value. The events are represented as categorical dependent variables, and the probability of a particular dependent variable being 1 is given using the logit function:

 

Before going into the details of how we can use logistic regression for classification, let's examine the logit function (also called the sigmoid function because of its S-shaped curve). The following diagram shows thelogit function and its derivative varies with respect to the input X, the Sigmoidal function (blue) and its derivative (orange):

A few important things to note from this diagram are the following...