## Questions and Answers

What strategy is proposed to improve the classification tree?

What is the purpose of cost complexity pruning?

What is the role of the tuning parameter 𝛼 in cost complexity pruning?

How is the value of 𝛼 chosen in the cost complexity pruning algorithm?

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What is the purpose of step 3 in the cost complexity pruning algorithm?

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What is the result of applying the cost complexity pruning to a large tree?

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What is the goal of the cost complexity pruning algorithm?

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What is the relationship between 𝛼 and the subtree T?

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What is the advantage of using cost complexity pruning over considering every possible subtree?

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What is the role of k-fold cross-validation in the cost complexity pruning algorithm?

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## Study Notes

### Tree Pruning

- The tuning parameter α controls the trade-off between subtree complexity and its fit to the training data.
- When α = 0, the subtree T will simply equal T0.

### Cost Complexity Pruning

- Cost complexity pruning is a method to select a small set of subtrees for consideration.
- It is also known as weakest link pruning.
- The algorithm for cost complexity pruning involves:
- Growing a large tree using recursive binary splitting and stopping according to the stopping condition.
- Applying cost complexity pruning to obtain a sequence of best subtrees as a function of α.
- Using k-fold cross-validation to choose α.
- Returning the subtree that corresponds to the chosen value of α.

### Classification Trees

- A classification tree is used to predict a qualitative response.
- The classification error rate is the fraction of training observations in a region that do not belong to the most common class.
- The classification error rate is not sufficient for tree-growing, and alternative measures are preferable.

### Gini Index

- The Gini index is a measure of total variance across K classes.
- It takes on a small value if all the p_mk's are close to zero or one.
- The Gini index is a measure of node purity, with a small value indicating that a node contains predominantly observations from a single class.

### Entropy

- An alternative to the Gini index is entropy, given by the formula -∑p_mk log p_mk.
- The entropy takes on a value near zero if the p_mk's are all near zero or near one.
- The Gini index and entropy are quite similar numerically.

### Tree Pruning Strategy

- A better strategy is to grow a very large tree T0 and then prune it back to obtain a subtree.
- This approach is preferable because it allows for a more exhaustive search of possible subtrees.

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## Description

Quiz about decision tree pruning, including the tuning parameter alpha and its effects on subtree complexity and fit to training data.