We've explored the structure of decision trees, their branches representing questions and their nodes as points of decision. Now, let's see how these elegant structures help us make predictions, much like a seasoned explorer uses their knowledge of the terrain to navigate the forest.
To make a prediction for a new, unseen data point, we simply follow the path from the root of the tree down to a leaf. At each internal node, we ask the question associated with that node and choose the branch that corresponds to the answer for our data point. We continue this process until we reach a leaf node. The prediction made by the tree is then the value or class assigned to that leaf.
graph TD
A[Root Node: Is it raining?] -->|Yes| B(Node 1: Is it windy?)
A -->|No| C(Node 2: Is it cold?)
B -->|Yes| D{Leaf: Stay Inside}
B -->|No| E{Leaf: Take Umbrella}
C -->|Yes| F{Leaf: Wear a Coat}
C -->|No| G{Leaf: Go Outside}
Let's imagine we have a new data point: 'Is it raining? Yes', 'Is it windy? No'. We start at the root node. The question is 'Is it raining?'. Our data point answers 'Yes'. So, we follow the 'Yes' branch to Node 1, which asks 'Is it windy?'. Our data point answers 'No'. We follow the 'No' branch from Node 1, and we arrive at Leaf node 'Take Umbrella'. Therefore, the decision tree predicts that we should 'Take Umbrella'.
For classification trees (like the one above), the leaf nodes typically represent class labels (e.g., 'Spam' or 'Not Spam', 'Cat' or 'Dog'). For regression trees, which predict continuous numerical values, the leaf nodes would contain the predicted numerical value, often the average of the target values of the training data points that ended up in that leaf.
The simplicity of this traversal is a key strength of decision trees. It's intuitive and easy to understand why a particular prediction was made, making them a great starting point for understanding predictive modeling.