As our decision tree grows deeper, it becomes a formidable fortress of rules, capable of classifying even the most complex data with impressive accuracy on the data it was trained on. However, this very depth can be a double-edged sword. We call this phenomenon 'overfitting'. Imagine a student memorizing every single answer to a practice test. They might ace that specific test, but if the actual exam has slightly different questions, they'll struggle. Similarly, an overfit decision tree has learned the training data 'too well', including its noise and peculiar patterns. This means it will likely perform poorly on new, unseen data.
The core problem of overfitting in decision trees is that they can become overly complex, creating branches and splits that are specific to individual training examples rather than generalizable patterns. This leads to high accuracy on the training set but poor performance on the test set. Think of it as drawing a line that perfectly traces every single dot in a scattered plot, including the outliers, instead of drawing a line that captures the general trend.
graph TD
A[Training Data] --> B{Decision Tree};
B --> C[High Accuracy on Training Data];
B --> D[Low Accuracy on New Data];
D --> E(Overfitting);
C --> E;
To combat this, we employ a technique called 'pruning'. Pruning is like carefully trimming the overgrown branches of our decision tree to simplify it. The goal is to remove branches that are unlikely to improve the tree's ability to generalize to new data. We do this by identifying and removing nodes that contribute little to the overall predictive power, effectively making the tree more robust and less susceptible to the noise in the training data.
There are several strategies for pruning. One common approach is 'pre-pruning', where we set limits on the tree's growth before it fully develops. This can involve stopping the splitting process when a node reaches a certain depth, when the number of samples in a node falls below a threshold, or when further splits don't significantly improve a chosen metric like information gain.
Another powerful technique is 'post-pruning'. Here, the tree is allowed to grow to its full potential first. Then, we go back and 'trim' it. A common post-pruning method involves evaluating whether removing a particular subtree (and replacing it with a leaf node) would actually improve the tree's performance on a validation set. If it does, we perform the prune. This often involves a process of cost-complexity pruning, where we balance the tree's complexity against its error rate.