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Functional form estimation using oblique projection matrices for ls-SVM regression models

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dc.creatorCaicedo Dorado, Alexander
dc.creatorVaron, Carolinaspa
dc.creatorVan Huffel, Sabinespa
dc.creatorSuykens, Johan A. K.spa
dc.date.accessioned2020-05-25T23:58:17Z
dc.date.available2020-05-25T23:58:17Z
dc.date.created2019spa
dc.description.abstractKernel regression models have been used as non-parametric methods for fitting experimental data. However, due to their non-parametric nature, they belong to the so-called 'black box' models, indicating that the relation between the input variables and the output, depending on the kernel selection, is unknown. In this paper we propose a new methodology to retrieve the relation between each input regressor variable and the output in a least squares support vector machine (LS-SVM) regression model. The method is based on oblique subspace projectors (ObSP), which allows to decouple the influence of input regressors on the output by including the undesired variables in the null space of the projection matrix. Such functional relations are represented by the nonlinear transformation of the input regressors, and their subspaces are estimated using appropriate kernel evaluations. We exploit the properties of ObSP in order to decompose the output of the obtained regression model as a sum of the partial nonlinear contributions and interaction effects of the input variables, we called this methodology Nonlinear ObSP (NObSP). We compare the performance of the proposed algorithm with the component selection and smooth operator (COSSO) for smoothing spline ANOVA models. We use as benchmark 2 toy examples and a real life regression model using the concrete strength dataset from the UCI machine learning repository. We showed that NObSP is able to outperform COSSO, producing stable estimations of the functional relations between the input regressors and the output, without the use of prior-knowledge. This methodology can be used in order to understand the functional relations between the inputs and the output in a regression model, retrieving the physical interpretation of the regression models. © 2019 Caicedo et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.eng
dc.format.mimetypeapplication/pdf
dc.identifier.doihttps://doi.org/10.1371/journal.pone.0217967
dc.identifier.issn1932-6203
dc.identifier.urihttps://repository.urosario.edu.co/handle/10336/22835
dc.language.isoengspa
dc.publisherPublic Library of Sciencespa
dc.relation.citationIssueNo. 6
dc.relation.citationTitlePLoS ONE
dc.relation.citationVolumeVol. 14
dc.relation.ispartofPLoS ONE, ISSN:19326203, Vol.14, No.6 (2019)spa
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85067381270&doi=10.1371%2fjournal.pone.0217967&partnerID=40&md5=a0bbb2bd48d46bdbdc95d15b265f2fedspa
dc.rights.accesRightsinfo:eu-repo/semantics/openAccess
dc.rights.accesoAbierto (Texto Completo)spa
dc.source.instnameinstname:Universidad del Rosariospa
dc.source.reponamereponame:Repositorio Institucional EdocURspa
dc.subject.keywordAnalysis of variancespa
dc.subject.keywordArticlespa
dc.subject.keywordStatisticaleng
dc.subject.keywordDecompositionspa
dc.subject.keywordHumanspa
dc.subject.keywordLeast square analysisspa
dc.subject.keywordSupport vector machinespa
dc.subject.keywordAlgorithmspa
dc.subject.keywordArtificial intelligencespa
dc.subject.keywordLeast square analysisspa
dc.subject.keywordMachine learningspa
dc.subject.keywordStatistical modelspa
dc.subject.keywordSupport vector machinespa
dc.subject.keywordAlgorithmsspa
dc.subject.keywordArtificial intelligencespa
dc.subject.keywordLeast-squares analysisspa
dc.subject.keywordMachine learningspa
dc.subject.keywordModelseng
dc.subject.keywordSupport vector machinespa
dc.titleFunctional form estimation using oblique projection matrices for ls-SVM regression modelsspa
dc.typearticleeng
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersion
dc.type.spaArtículospa
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