We have been discussing two important questions:

• How does it decide the threshold for splitting a variable?
• How does a decision tree determine which variable to use for splitting?

Now that we have covered fundamental concepts such as impurity calculation using entropy, Gini, and variance, as well as the computation of information gain, it is time to address these questions.

How Does a Decision Tree Determine the Threshold for Splitting a Variable

Variables can be either continuous or discrete. Let's first examine the case of continuous variables. The process for selecting the optimal threshold for a continuous variable involves the following steps:

• Sort the variable values.
• Compute the information gain for each possible threshold.
• Choose the threshold that yields the maximum information gain.

For discrete variables, compute the information gain for each unique value and select the category that provides the highest information gain.

How Does a Decision Tree Select the Best Variable for Splitting

The process for selecting the best variable for splitting involves the following steps:

• Identify the best threshold for each variable using the method described above.
• Choose the variable that results in the highest information gain.