Tree-Based Methods

Regressioin

It might be a overfit if we have a huge tree since we have fitted the model so well to the training data set. We need a termination condition, or we simple build a large tree then prune it to a smaller one.

Cost complexity pruning: add a punishment to the cost function

\sum_{t} \sum_i (y_i - \tilde y_i)^2 + \alpha t

where \alpha can be determined from cross validation.

Categorical

  1. Gini index: purity
  2. Cross entropy

Tree vs Linear Regression

  1. Trees are box based

Bagging

Bootstrap aggregation

For categorical

  1. Majority voting: most frequent categorical predictions
  2. Average

References and Notes


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