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Publication type: Article in scientific journal
Type of review: Peer review (publication)
Title: Estimating neural network’s performance with bootstrap : a tutorial
Authors: Michelucci, Umberto
Venturini, Francesca
et. al: No
DOI: 10.3390/make3020018
Published in: Machine Learning and Knowledge Extraction
Volume(Issue): 3
Issue: 2
Page(s): 357
Pages to: 373
Issue Date: 2021
Publisher / Ed. Institution: MDPI
ISSN: 2504-4990
Language: English
Subjects: Neural network; Machine learning; Bootstrap; Resampling; Algorithm
Subject (DDC): 006: Special computer methods
Abstract: Neural networks present characteristics where the results are strongly dependent on the training data, the weight initialisation, and the hyperparameters chosen. The determination of the distribution of a statistical estimator, as the Mean Squared Error (MSE) or the accuracy, is fundamental to evaluate the performance of a neural network model (NNM). For many machine learning models, as linear regression, it is possible to analytically obtain information as variance or confidence intervals on the results. Neural networks present the difficulty of not being analytically tractable due to their complexity. Therefore, it is impossible to easily estimate distributions of statistical estimators. When estimating the global performance of an NNM by estimating the MSE in a regression problem, for example, it is important to know the variance of the MSE. Bootstrap is one of the most important resampling techniques to estimate averages and variances, between other properties, of statistical estimators. In this tutorial, the application of resampling techniques (including bootstrap) to the evaluation of neural networks’ performance is explained from both a theoretical and practical point of view. The pseudo-code of the algorithms is provided to facilitate their implementation. Computational aspects, as the training time, are discussed, since resampling techniques always require simulations to be run many thousands of times and, therefore, are computationally intensive. A specific version of the bootstrap algorithm is presented that allows the estimation of the distribution of a statistical estimator when dealing with an NNM in a computationally effective way. Finally, algorithms are compared on both synthetically generated and real data to demonstrate their performance.
Fulltext version: Published version
License (according to publishing contract): CC BY 4.0: Attribution 4.0 International
Departement: School of Engineering
Organisational Unit: Institute of Applied Mathematics and Physics (IAMP)
Appears in collections:Publikationen School of Engineering

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