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…
8 Citations
An Adaptively Resized Parametric Bootstrap for Inference in High-dimensional Generalized Linear Models
- Economics, Computer Science
- 2022
It is demonstrated that the resized bootstrap method yields valid confidence intervals in both simulated and real data examples, and the methods extend to other high-dimensional generalized linear models.
On Uncertainty Estimation by Tree-based Surrogate Models in Sequential Model-based Optimization
- Computer ScienceAISTATS
- 2022
A new way of con-structing an ensemble of randomized trees is proposed, referred to as BwO forest, where bagging with oversampling is employed to construct boot-strapped samples that are used to build randomized trees with random splitting.
Regularization Guarantees Generalization in Bayesian Reinforcement Learning through Algorithmic Stability
- Mathematics, Computer ScienceAAAI
- 2022
This work shows that regularized MDPs satisfy a certain quadratic growth criterion, which is sufficient to establish stability, and allows us to study the effect of regularization on generalization in the Bayesian RL setting.
Sub-sampling for Efficient Non-Parametric Bandit Exploration
- Computer ScienceNeurIPS
- 2020
In this paper we propose the first multi-armed bandit algorithm based on re-sampling that achieves asymptotically optimal regret simultaneously for different families of arms (namely Bernoulli,…
Bootstraps Regularize Singular Correlation Matrices
- Mathematics
- 2020
I show analytically that the average of $k$ bootstrapped correlation matrices rapidly becomes positive-definite as $k$ increases, which provides a simple approach to regularize singular Pearson…
Inferring the Joint Demographic History of Multiple Populations: Beyond the Diffusion Approximation
- BiologyGenetics
- 2017
A tractable model of ordinary differential equations for the evolution of allele frequencies that is closely related to the diffusion approximation but avoids many of its limitations and approximations is proposed.
Estimating helminth burdens using sibship reconstruction
- BiologyParasites & Vectors
- 2019
This work developed a novel statistical method for estimating female worm burdens from data on the number of unique female parental genotypes derived from sibship reconstruction, and illustrates the approach using genotypic data on Schistosoma mansoni (miracidial) offspring collected from schoolchildren in Tanzania.
Reliable BIER With Peer Caching
- Computer ScienceIEEE Transactions on Network and Service Management
- 2019
Results indicate that local peer recovery is able to substantially reduce the overall retransmission traffic, and that this can be achieved through simple policies, where no signalling is required to build a set of candidate peers.
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.
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.…
Identification of outlier bootstrap samples
- Computer Science
- 1997
We define a variation of Efron's method II based on the outlier bootstrap sample concept. A criterion for the identification of such samples is given, with which a variation in the bootstrap sample…
Two Rules of Thumb for the Approximation of the Binomial Distribution by the Normal Distribution
- Mathematics
- 1989
In this department The American Statistician publishes articles, reviews, under the section heading. Articles and notes for the department, but not and notes of interest to teachers of the first…