Pruning In Decision Tree

(1) What Is Pruning?

Pruning is a technique used in decision trees to reduce overfitting and improve the generalization ability of the model.
It involves removing branches or nodes from the tree that do not contribute significantly to its predictive accuracy.
Pruning helps simplify the tree structure, making it less complex and easier to interpret.
There are two main types of pruning techniques:

Pre-pruning involves stopping the growth of the decision tree before it becomes fully expanded. It applies stopping criteria during the construction process to determine when to stop splitting and create leaf nodes instead.
Common pre-pruning stopping criteria include:
- Maximum Depth: Limiting the maximum depth or number of levels of the tree.
- Minimum Number of Samples per Leaf: Requiring a minimum number of instances in a leaf node to allow splitting.
- Minimum Impurity Decrease: Requiring a minimum improvement in impurity (e.g., Gini index or entropy) to allow a split.
Pre-pruning helps reduce the risk of overfitting by preventing the tree from becoming overly complex and capturing noise or irrelevant patterns in the data.

Post-pruning, also known as backward pruning or cost-complexity pruning, involves growing the decision tree to its full size and then selectively removing branches or nodes.
The idea behind post-pruning is to evaluate the impact of removing a node or branch on the tree’s performance using a validation dataset or a suitable evaluation metric.
The pruning decision is typically based on a statistical measure, such as error rate, accuracy, or cross-validated error estimate.
If removing a subtree improves the evaluation metric, the subtree is pruned, and the parent node becomes a leaf node with the most common class label or the average value for regression tasks.
This process is repeated iteratively, evaluating the impact of pruning at each step, until further pruning deteriorates the model’s performance.
Post-pruning is more computationally expensive than pre-pruning but can often lead to more accurate and simpler decision trees.

When performing post-pruning on decision trees, various evaluation metrics can be used to assess the impact of pruning and guide the decision-making process.
Here are some common evaluation metrics used in post-pruning:

The error rate, also known as the misclassification rate, measures the proportion of misclassified instances in the dataset.
It is calculated as the number of misclassified instances divided by the total number of instances.
When pruning a decision tree, the error rate of the pruned tree is compared to the error rate of the original tree.
If the pruned tree has a lower error rate, the pruning is considered beneficial.

Accuracy represents the proportion of correctly classified instances in the dataset.
It is calculated as the number of correctly classified instances divided by the total number of instances.
Similar to the error rate, the accuracy of the pruned tree is compared to the accuracy of the original tree to evaluate the effectiveness of pruning.
A higher accuracy indicates improved performance.

Cross-validation is a technique used to estimate the performance of a model on unseen data.
It involves splitting the dataset into multiple subsets (folds), training the model on a subset, and evaluating it on the remaining fold.
This process is repeated several times, with different folds used for training and evaluation.
The cross-validated error estimate, such as cross-validated error rate or cross-validated accuracy, provides a more robust and unbiased evaluation of the decision tree’s performance.
Pruning is evaluated based on the cross–validated error estimate, comparing the pruned tree’s performance to the original tree.

Information criteria, such as the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC), provide a trade-off between model complexity and fit to the data.
These criteria penalize models with higher complexity, encouraging the selection of simpler models that still provide a good fit to the data.
The AIC or BIC values are compared between the pruned tree and the original tree, with lower values indicating a better balance between complexity and fit.

Pruning helps prevent overfitting, improves model interpretability, and reduces the risk of the decision tree capturing noise or irrelevant patterns.
It strikes a balance between model complexity and generalization, resulting in a more robust and reliable model.