Decision trees are a popular machine learning algorithm used for both regression and classification problems. Decision trees work by recursively partitioning the input space into smaller and smaller regions based on the values of the input variables, until each region contains observations of only one class or has a homogeneous output value.
The basic idea behind decision trees is to build a tree-like model where each node represents a feature or attribute, each branch represents a decision rule based on the value of that feature or attribute, and each leaf node represents a class or output value. The tree is built by selecting the best feature or attribute to split the data based on a criterion such as information gain or Gini impurity.
When a new observation is presented to the model, it is classified by traversing the decision tree from the root node to a leaf node. At each node, the decision rule based on the value of the corresponding feature is applied to determine which branch to follow. When a leaf node is reached, the class or output value associated with that node is returned as the predicted value.
Decision trees have several advantages, including their ability to handle both numerical and categorical data, their interpretability and visualizability, and their ability to handle missing data. They are also relatively fast and easy to train compared to other more complex machine learning algorithms.
However, decision trees can suffer from overfitting, where the model becomes too complex and fits the noise in the data rather than the underlying pattern. To avoid overfitting, techniques such as pruning and ensemble methods like random forests can be used.