# What is the distribution of the number of unique original items in a bootstrap sample

@article{Mendelson2016WhatIT, title={What is the distribution of the number of unique original items in a bootstrap sample}, author={Alex F. Mendelson and Maria A. Zuluaga and Brian F. Hutton and S{\'e}bastien Ourselin}, journal={arXiv: Machine Learning}, year={2016} }

Sampling with replacement occurs in many settings in machine learning, notably in the bagging ensemble technique and the .632+ validation scheme. The number of unique original items in a bootstrap sample can have an important role in the behaviour of prediction models learned on it. Indeed, there are uncontrived examples where duplicate items have no effect. The purpose of this report is to present the distribution of the number of unique original items in a bootstrap sample clearly and…

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## References

SHOWING 1-10 OF 21 REFERENCES

### Analyzing Bagging

- Computer Science
- 2001

This work formalizes the notion of instability and derive theoretical results to analyze the variance reduction effect of bagging (or variants thereof) in mainly hard decision problems, which include estimation after testing in regression and decision trees for regression functions and classifiers.

### Improvements on Cross-Validation: The 632+ Bootstrap Method

- Computer Science
- 1997

It is shown that a particular bootstrap method, the .632+ rule, substantially outperforms cross-validation in a catalog of 24 simulation experiments and also considers estimating the variability of an error rate estimate.

### Bias of the Random Forest Out-of-Bag (OOB) Error for Certain Input Parameters

- Computer Science
- 2011

Simulation studies are performed to compare the effect of the input parameters on the predictive ability of the random forest, and it is found that the number of variables sampled, m-try, has the largest impact on the true prediction error.

### Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap

- EconomicsComput. Stat. Data Anal.
- 2009

### Bagging predictors

- Computer ScienceMachine Learning
- 2004

Tests on real and simulated data sets using classification and regression trees and subset selection in linear regression show that bagging can give substantial gains in accuracy.

### OUT-OF-BAG ESTIMATION

- Mathematics
- 1996

In bagging, predictors are constructed using bootstrap samples from the training set and then aggregated to form a bagged predictor. Each bootstrap sample leaves out about 37% of the examples. These…

### Random Forests

- Computer ScienceMachine Learning
- 2004

Internal estimates monitor error, strength, and correlation and these are used to show the response to increasing the number of features used in the forest, and are also applicable to regression.

### On the Failure of the Bootstrap for Matching Estimators

- Mathematics, Economics
- 2006

Matching estimators are widely used in empirical economics for the evaluation of programs or treatments. Researchers using matching methods often apply the bootstrap to calculate the standard errors.…