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Questions and Answers
What is the purpose of leaf nodes in a decision tree?
In a regression tree, what is used to predict the outcome in a region?
What is the initial node in a decision tree called?
Which type of problems can tree-based methods be applied to?
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What does bagging refer to in the context of building trees?
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How are decision nodes navigated in a decision tree?
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What is the purpose of making predictions in the region Rj of a classification tree?
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How is the split level determined for each rectangle R in the context of decision trees?
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What is the advantage of decision trees over other regression and classification approaches?
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When would linear regression outperform regression trees according to the text?
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What can result from a small change in the training data when using decision trees?
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How are decision trees different from linear regression with regard to handling qualitative predictors?
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Study Notes
Decision Trees
- A decision tree starts with a single root node and consists of decision nodes, which split into two or more subnodes based on features of a data set.
- The tree is navigated via if-then rules, with leaf nodes representing prediction outputs for the model.
Tree-Based Methods
- Can be applied to regression and classification problems.
- Involve stratifying or segmenting the predictor space into simple regions.
- Predictions are made using the mean or mode of the training observations in each region.
Regression Trees
- Used for predicting continuous outcomes (e.g. baseball players' salaries).
- Basic steps:
- Divide the predictor space into distinct and non-overlapping regions.
- Make the same prediction for every observation in each region, which is the mean of the response values for the training observations in that region.
Classification Trees
- Used for predicting categorical outcomes (e.g. wine ratings).
- Basic steps:
- Divide the predictor space into distinct and non-overlapping regions.
- Make the same prediction for every observation in each region, which is the category with the majority of observations in that region.
Gini Impurity
- A measure used to decide on the split level in a tree.
- Calculated as I(R) = 1 - sum (p_k)^2, where p_k is the proportion of observations in a rectangle R that belong to class k.
- Used to compare the reduction in this measure across all splits and predictor variables.
Advantages and Disadvantages of Decision Trees
- Advantages:
- Easy to explain and interpret.
- Can handle qualitative predictors without dummy variables.
- Disadvantages:
- Generally have lower predictive accuracy than other approaches.
- Can be non-robust to changes in the training data.
Decision Trees vs. Linear Regression
- If the relationship between predictors and response is linear, linear regression may outperform decision trees.
- If the relationship is non-linear, decision trees may outperform classical approaches.
- Decision trees can use a feature multiple times in the same model.
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Description
Test your knowledge on the structure and building steps of a decision tree, including Gini impurity, pruning, bagging, and random forests. Learn about how decision trees start with a root node and navigate through decision nodes based on if-then rules.
