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Bootstrap

What is bootstrap for?

Bootstrap is most commonly used for which of the following?

  1. Assessing estimator variance.

  2. Assessing estimator bias.

  3. Assessing estimator error.

Solutions

The first. Bias and error are hard.

Bootstrap and the Bayes optimal classifier

Let y^\hat y denote an estimator for the Bayes optimal classifier. Given a dataset with two predictors, a user creates 10 bootstrap datasets and fits the estimator to each one, leading to 10 fits in all. The user then visualizes the decision boundary for each fit. They use this to help guide their intuition about the estimator’s variability due to randomness in the training dataset. True or false: the user will reach meaningless conclusions because estimator variance is undefined in this context.

Solutions

False. It is actually true that estimator variance is undefined in this context (y^\hat y isn’t a number). However, the user’s procedure may still be helpful for visualizing how much y^\hat y varies from dataset to dataset.

Unsupervised learning
Dimensionality reduction
The quality of your estimator
Cross-validation