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# Decision Tree Pruning

Created by
@EliteAsh

## Questions and Answers

### What strategy is proposed to improve the classification tree?

• Use k-fold cross-validation to evaluate the tree
• Grow a small tree and then expand it
• Use a random forest to combine multiple trees
• Grow a very large tree and then prune it back to obtain a subtree (correct)
• ### What is the purpose of cost complexity pruning?

• To grow a very large tree
• To select a small set of subtrees for consideration (correct)
• To determine the best way to split the tree
• To evaluate the test error for the left fold
• ### What is the role of the tuning parameter 𝛼 in cost complexity pruning?

• To evaluate the MSE for the test error
• To combine multiple trees
• To determine the stopping condition for growing the tree
• To index a sequence of trees (correct)
• ### How is the value of 𝛼 chosen in the cost complexity pruning algorithm?

<p>By using k-fold cross-validation to minimize the average error</p> Signup and view all the answers

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

<p>To evaluate the MSE for the test error for the left fold</p> Signup and view all the answers

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

<p>A sequence of best subtrees as a function of 𝛼</p> Signup and view all the answers

### What is the goal of the cost complexity pruning algorithm?

<p>To find the subtree that minimizes the average error</p> Signup and view all the answers

### What is the relationship between 𝛼 and the subtree T?

<p>T is a subset of T0 and has the smallest possible error</p> Signup and view all the answers

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

<p>It allows for a more efficient search of the subtree space</p> Signup and view all the answers

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

<p>To choose the value of 𝛼</p> Signup and view all the answers

## 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.

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