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Open AccessArticle

A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap

1
Department of Mathematics, University of Pavia, 27100 Pavia, Italy
2
Department of Political and Social Sciences, University of Pavia, 27100 Pavia, Italy
3
Department of Decision Sciences, Bocconi University, 20100 Milano, Italy
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 9 December 2020 / Revised: 21 December 2020 / Accepted: 29 December 2020 / Published: 3 January 2021
Bootstrap resampling techniques, introduced by Efron and Rubin, can be presented in a general Bayesian framework, approximating the statistical distribution of a statistical functional ϕ(F), where F is a random distribution function. Efron’s and Rubin’s bootstrap procedures can be extended, introducing an informative prior through the Proper Bayesian bootstrap. In this paper different bootstrap techniques are used and compared in predictive classification and regression models based on ensemble approaches, i.e., bagging models involving decision trees. Proper Bayesian bootstrap, proposed by Muliere and Secchi, is used to sample the posterior distribution over trees, introducing prior distributions on the covariates and the target variable. The results obtained are compared with respect to other competitive procedures employing different bootstrap techniques. The empirical analysis reports the results obtained on simulated and real data. View Full-Text
Keywords: bootstrap; Bayesian nonparametric learning; ensemble models bootstrap; Bayesian nonparametric learning; ensemble models
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MDPI and ACS Style

Galvani, M.; Bardelli, C.; Figini, S.; Muliere, P. A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap. Algorithms 2021, 14, 11. https://0-doi-org.brum.beds.ac.uk/10.3390/a14010011

AMA Style

Galvani M, Bardelli C, Figini S, Muliere P. A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap. Algorithms. 2021; 14(1):11. https://0-doi-org.brum.beds.ac.uk/10.3390/a14010011

Chicago/Turabian Style

Galvani, Marta; Bardelli, Chiara; Figini, Silvia; Muliere, Pietro. 2021. "A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap" Algorithms 14, no. 1: 11. https://0-doi-org.brum.beds.ac.uk/10.3390/a14010011

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