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FRM Part I · FRM Exam Part I · Machine Learning and Prediction

A random forest has 200 trees, each trained on a bootstrap sample of n = 1,000 observations. Approximately what fraction of observations is out-of-bag for any given tree, and what is the use of these observations?

About 36.8% of observations are out-of-bag for each tree, since (1−1/n)^n approaches e^−1. Because these were not used to fit that tree, predicting them gives a built-in estimate of out-of-sample error without a separate validation set.

  1. AAbout 63.2%; they are used to train the tree's splits
  2. BAbout 36.8%; they provide a built-in estimate of out-of-sample errorCorrect
  3. CAbout 36.8%; they are discarded because they add bias
  4. DAbout 63.2%; they provide a built-in estimate of out-of-sample error

Explanation

The probability an observation is never drawn in n draws with replacement is (1−1/n)^n ≈ e^−1 ≈ 0.368. Those out-of-bag observations were not used to fit that tree, so predictions on them estimate out-of-sample error. The 63.2% figure is the in-bag share, which is the distractor.

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