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.
Algorithms 2021, 14(1), 11; https://0-doi-org.brum.beds.ac.uk/10.3390/a14010011
Received: 9 December 2020 / Revised: 21 December 2020 / Accepted: 29 December 2020 / Published: 3 January 2021
(This article belongs to the Special Issue Bayesian Networks: Inference Algorithms, Applications, and Software Tools)
Bootstrap resampling techniques, introduced by Efron and Rubin, can be presented in a general Bayesian framework, approximating the statistical distribution of a statistical functional , 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
▼
Show Figures
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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 StyleGalvani, 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
Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
Search more from Scilit