How do you pruning cost complexity?

How do you pruning cost complexity?

Cost-Complexity Pruning

1. need to optimize the cost-complexity function.
2. Rα(T)=R(T)+α⋅|f(T)| where. R(T) is the training/learning error. f(T) a function that returns the set of leaves of tree T.
3. R(T)=∑t∈f(T)r(t)⋅p(t)=∑t∈f(T)R(t) ∑t∈f(T)R(t) – sum of misclassification errors at each leaf.

What is the best way to find Alpha for cost complexity pruning?

1. Train tree on entire training data.
2. Calculate sequence of subtrees S and αs A to test.
3. Apply inner crossvalidation.
4. Select α with best performance based on inner crossvalidation.
5. Find subtree in the sequence S built based on entire training data for that α
6. Return that subtree.

Why is cost complexity pruning preferred?

It reduces the size of a Decision Tree which might slightly increase your training error but drastically decrease your testing error, hence making it more adaptable. Minimal Cost-Complexity Pruning is one of the types of Pruning of Decision Trees.

Does pruning decrease complexity?

Pruning reduces the complexity of the final classifier, and hence improves predictive accuracy by the reduction of overfitting. There are many techniques for tree pruning that differ in the measurement that is used to optimize performance.

What is cost complexity?

Cost of complexity is a term often used to describe the costs that are caused by introducing new products and managing the variety of products produced. Many different products would cause a high cost of complexity, fewer and more similar products a low cost of complexity.

What is cost complexity parameter?

The complexity parameter (cp) is used to control the size of the decision tree and to select the optimal tree size. If the cost of adding another variable to the decision tree from the current node is above the value of cp, then tree building does not continue.

What is complexity in decision tree?

The decision tree complexity of a function is the minimum depth of a decision tree that computes that function. A property is evasive if its decision tree complexity is equal to the number of variables.

How is complexity parameter calculated?

cp: Complexity Parameter The complexity parameter (cp) in rpart is the minimum improvement in the model needed at each node. For the given tree, add up the misclassification at every terminal node. Then multiply the number of splits time a penalty term (lambda) and add it to the total misclassification.

How to calculate the cost complexity of a pruned tree?

The complexity is simply the number of nodes in the pruned tree. So the cost-complexity is a combination of the cost of the tree and the weighted size. To the find the optimal complexity weight, one can do something such as cross-validation. Also, return a list of the sizes for each cost-complexity.

When to use cost-complexity pruning combined with cross validation?

We will later use cost-complexity pruning combined with cross validation to keep the model from overfitting. The result of the pruned model is the following: We see that there is a small amount of unwanted blue in the upper right, but most of the unwanted variation is gone.

How to reduce the complexity of a decision tree?

In DecisionTreeClassifier, this pruning technique is parameterized by the cost complexity parameter, ccp_alpha. Greater values of ccp_alpha increase the number of nodes pruned.

How is the biggest tree chosen for pruning?

If α = 0 then the biggest tree will be chosen because the complexity penalty term is essentially dropped. As α approaches infinity, the tree of size 1, i.e., a single root node, will be selected.