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Random Forests

Dr. D’Agostino McGowan

1 / 4
Dr. Lucy D'Agostino McGowan adapted from slides by Hastie & Tibshirani

Random forests

Do you ❤️ all of the tree puns?

  • Random forests provide an improvement over bagged trees by way of a small tweak that decorrelates the trees
2 / 4
Dr. Lucy D'Agostino McGowan adapted from slides by Hastie & Tibshirani

Random forests

Do you ❤️ all of the tree puns?

  • Random forests provide an improvement over bagged trees by way of a small tweak that decorrelates the trees
  • By decorrelating the trees, this reduces the variance even more when we average the trees!
2 / 4
Dr. Lucy D'Agostino McGowan adapted from slides by Hastie & Tibshirani

Random Forest process

  • Like bagging, build a number of decision trees on bootstrapped training samples
3 / 4
Dr. Lucy D'Agostino McGowan adapted from slides by Hastie & Tibshirani

Random Forest process

  • Like bagging, build a number of decision trees on bootstrapped training samples
  • Each time the tree is split, instead of considering all predictors (like bagging), a random selection of \(m\) predictors is chosen as split candidates from the full set of \(p\) predictors
  • The split is allowed to use only one of those \(m\) predictors
3 / 4
Dr. Lucy D'Agostino McGowan adapted from slides by Hastie & Tibshirani

Random Forest process

  • Like bagging, build a number of decision trees on bootstrapped training samples
  • Each time the tree is split, instead of considering all predictors (like bagging), a random selection of \(m\) predictors is chosen as split candidates from the full set of \(p\) predictors
  • The split is allowed to use only one of those \(m\) predictors
  • A fresh selection of \(m\) predictors is taken at each split
3 / 4
Dr. Lucy D'Agostino McGowan adapted from slides by Hastie & Tibshirani

Random Forest process

  • Like bagging, build a number of decision trees on bootstrapped training samples
  • Each time the tree is split, instead of considering all predictors (like bagging), a random selection of \(m\) predictors is chosen as split candidates from the full set of \(p\) predictors
  • The split is allowed to use only one of those \(m\) predictors
  • A fresh selection of \(m\) predictors is taken at each split
  • typically we choose \(m \approx \sqrt{p}\)
3 / 4
Dr. Lucy D'Agostino McGowan adapted from slides by Hastie & Tibshirani
01:00

Choosing m for Random Forest

Let's say you have a dataset with 100 observations and 9 variables, if you were fitting a random forest, what would a good \(m\) be?

4 / 4
Dr. Lucy D'Agostino McGowan adapted from slides by Hastie & Tibshirani

Random forests

Do you ❤️ all of the tree puns?

  • Random forests provide an improvement over bagged trees by way of a small tweak that decorrelates the trees
2 / 4
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