Decision trees are constructed using a series of binary decisions on the input features to predict the target variable.
A decision tree consists of a root node, internal nodes, and leaf nodes. The root node represents the entire dataset, and each internal node represents a decision based on one of the input features. The edges of the tree represent the possible outcomes of each decision, and the leaf nodes represent the predicted output.
A decision tree classification algorithm uses a training dataset to stratify or segment the predictor space into multiple regions. Each such region has only a subset of the training dataset.
To predict the outcome for a given (test) observation, first, we determine which of these regions it belongs to. Once its region is identified, its outcome class is predicted as being the same as the mode (most common) of the outcome classes of all the training observations that are included in that region.
The algorithm works by recursively splitting the data into subsets based on the values of the input variables, with the goal of maximizing the information gain at each step. The resulting tree can be used to make predictions for new instances.
The tree consists of nodes and branches. The nodes represent a decision or a test on a particular attribute, and the branches represent the possible outcomes of the test. A sketch of the algorithm is as follows:
- Calculate the entropy of the entire dataset.
- For each input variable, calculate the information gain. The variable to split on is chosen based on the information gain, which measures the reduction in entropy or impurity achieved by splitting the data on that variable. The variable with the highest information gain is chosen as the splitting variable at each node.
- Choose the input variable with the highest information gain as the root node of the tree.
- For each possible value of the root node, create a new branch and recursively repeat steps 1–3 on the subset of the data that…