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Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems
Model selection criteria are widely used to identify the model that best represents the data among a set of potential candidates. Amidst the different model selection criteria, the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) are the most popular and better underst...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8464864/ https://www.ncbi.nlm.nih.gov/pubmed/34573827 http://dx.doi.org/10.3390/e23091202 |
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author | Spolladore, Luca Gelfusa, Michela Rossi, Riccardo Murari, Andrea |
author_facet | Spolladore, Luca Gelfusa, Michela Rossi, Riccardo Murari, Andrea |
author_sort | Spolladore, Luca |
collection | PubMed |
description | Model selection criteria are widely used to identify the model that best represents the data among a set of potential candidates. Amidst the different model selection criteria, the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) are the most popular and better understood. In the derivation of these indicators, it was assumed that the model’s dependent variables have already been properly identified and that the entries are not affected by significant uncertainties. These are issues that can become quite serious when investigating complex systems, especially when variables are highly correlated and the measurement uncertainties associated with them are not negligible. More sophisticated versions of this criteria, capable of better detecting spurious relations between variables when non-negligible noise is present, are proposed in this paper. Their derivation is obtained starting from a Bayesian statistics framework and adding an a priori Chi-squared probability distribution function of the model, dependent on a specifically defined information theoretic quantity that takes into account the redundancy between the dependent variables. The performances of the proposed versions of these criteria are assessed through a series of systematic simulations, using synthetic data for various classes of functions and noise levels. The results show that the upgraded formulation of the criteria clearly outperforms the traditional ones in most of the cases reported. |
format | Online Article Text |
id | pubmed-8464864 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-84648642021-09-27 Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems Spolladore, Luca Gelfusa, Michela Rossi, Riccardo Murari, Andrea Entropy (Basel) Article Model selection criteria are widely used to identify the model that best represents the data among a set of potential candidates. Amidst the different model selection criteria, the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) are the most popular and better understood. In the derivation of these indicators, it was assumed that the model’s dependent variables have already been properly identified and that the entries are not affected by significant uncertainties. These are issues that can become quite serious when investigating complex systems, especially when variables are highly correlated and the measurement uncertainties associated with them are not negligible. More sophisticated versions of this criteria, capable of better detecting spurious relations between variables when non-negligible noise is present, are proposed in this paper. Their derivation is obtained starting from a Bayesian statistics framework and adding an a priori Chi-squared probability distribution function of the model, dependent on a specifically defined information theoretic quantity that takes into account the redundancy between the dependent variables. The performances of the proposed versions of these criteria are assessed through a series of systematic simulations, using synthetic data for various classes of functions and noise levels. The results show that the upgraded formulation of the criteria clearly outperforms the traditional ones in most of the cases reported. MDPI 2021-09-11 /pmc/articles/PMC8464864/ /pubmed/34573827 http://dx.doi.org/10.3390/e23091202 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Spolladore, Luca Gelfusa, Michela Rossi, Riccardo Murari, Andrea Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems |
title | Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems |
title_full | Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems |
title_fullStr | Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems |
title_full_unstemmed | Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems |
title_short | Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems |
title_sort | improved treatment of the independent variables for the deployment of model selection criteria in the analysis of complex systems |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8464864/ https://www.ncbi.nlm.nih.gov/pubmed/34573827 http://dx.doi.org/10.3390/e23091202 |
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