Comparison of trivariate copula-based conditional quantile regression versus machine learning methods for estimating copper recovery

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dc.contributor.authorHernández, Heber
dc.contributor.authorDíaz Viera, Martín Alberto
dc.contributor.authorAlberdi Celaya, Elisabete
dc.contributor.authorGoti Elordi, Aitor
dc.date.accessioned2025-03-14T10:41:39Z
dc.date.available2025-03-14T10:41:39Z
dc.date.issued2025-02
dc.date.updated2025-03-14T10:41:39Z
dc.description.abstractIn this study, an innovative methodology using trivariate copula-based conditional quantile regression (CBQR) is proposed for estimating copper recovery. This approach is compared with six supervised machine learning regression methods, namely, Decision Tree, Extra Tree, Support Vector Regression (linear and epsilon), Multilayer Perceptron, and Random Forest. For comparison purposes, an open access database representative of a porphyry copper deposit is used. The database contains geochemical information on minerals, mineral zoning data, and metallurgical test results related to copper recovery by flotation. To simulate a high undersampling scenario, only 5% of the copper recovery information was used for training and validation, while the remaining 95% was used for prediction, applying in all these stages error metrics, such as R2, MaxRE, MAE, MSE, MedAE, and MAPE. The results demonstrate that trivariate CBQR outperforms machine learning methods in accuracy and flexibility, offering a robust alternative solution to model complex relationships between variables under limited data conditions. This approach not only avoids the need for intensive tuning of multiple hyperparameters, but also effectively addresses estimation challenges in scenarios where traditional methods are insufficient. Finally, the feasibility of applying this methodology to different data scales is evaluated, integrating the error associated with the change in scale as an inherent part of the estimation of conditioning variables in the geostatistical contexten
dc.description.sponsorshipThis work was funded by project SUSTASKILLS: Development of a roadmap for the implementation of skills related to industrial symbiosis and energy efficiency to achieve a sustainable process industry (Grant Agreement No PUE_2023_1_0006)en
dc.identifier.citationHernández, H., Díaz-Viera, M. A., Alberdi, E., & Goti, A. (2025). Comparison of trivariate copula-based conditional quantile regression versus machine learning methods for estimating copper recovery. Mathematics, 13(4). https://doi.org/10.3390/MATH13040576
dc.identifier.doi10.3390/MATH13040576
dc.identifier.eissn2227-7390
dc.identifier.urihttps://hdl.handle.net/20.500.14454/2532
dc.language.isoeng
dc.publisherMultidisciplinary Digital Publishing Institute (MDPI)
dc.rights© 2025 by the authors
dc.subject.otherCopula
dc.subject.otherKernel smoothing
dc.subject.otherMachine learning
dc.subject.otherMetallurgical copper recovery
dc.subject.otherQuantile regression
dc.titleComparison of trivariate copula-based conditional quantile regression versus machine learning methods for estimating copper recoveryen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.issue4
oaire.citation.titleMathematics
oaire.citation.volume13
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
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