CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization

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dc.contributor.authorWeber, Gerhard-Wilhelm
dc.contributor.authorBatmaz, Inci
dc.contributor.authorKoksal, Gulser
dc.contributor.authorTaylan, Pakize
dc.contributor.authorYerlikaya-Ozkurt, Fatma
dc.date.accessioned2024-04-24T17:07:52Z
dc.date.available2024-04-24T17:07:52Z
dc.date.issued2012
dc.departmentDicle Üniversitesien_US
dc.description.abstractRegression analysis is a widely used statistical method for modelling relationships between variables. Multivariate adaptive regression splines (MARS) especially is very useful for high-dimensional problems and fitting nonlinear multivariate functions. A special advantage of MARS lies in its ability to estimate contributions of some basis functions so that both additive and interactive effects of the predictors are allowed to determine the response variable. The MARS method consists of two parts: forward and backward algorithms. Through these algorithms, it seeks to achieve two objectives: a good fit to the data, but a simple model. In this article, we use a penalized residual sum of squares for MARS as a Tikhonov regularization problem, and treat this with continuous optimization technique, in particular, the framework of conic quadratic programming. We call this new approach to MARS as CMARS, and consider it as becoming an important complementary and model-based alternative to the backward stepwise algorithm. The performance of CMARS is also evaluated using different data sets with different features, and the results are discussed.en_US
dc.description.sponsorshipTurkish Scientific and Technological Research Institute (TUBITAK) [105M138]en_US
dc.description.sponsorshipThis study is supported by the Turkish Scientific and Technological Research Institute (TUBITAK) under the project number 105M138. One of the authors, Fatma Yerlikaya-Ozkurt, has been supported by the TUBITAK Domestic Doctoral Scholarship Program.en_US
dc.identifier.doi10.1080/17415977.2011.624770
dc.identifier.endpage400en_US
dc.identifier.issn1741-5977
dc.identifier.issn1741-5985
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-84860334238
dc.identifier.scopusqualityQ3
dc.identifier.startpage371en_US
dc.identifier.urihttps://doi.org/10.1080/17415977.2011.624770
dc.identifier.urihttps://hdl.handle.net/11468/17057
dc.identifier.volume20en_US
dc.identifier.wosWOS:000303213600006
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoenen_US
dc.publisherTaylor & Francis Ltden_US
dc.relation.ispartofInverse Problems in Science and Engineering
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectTikhonov Regularizationen_US
dc.subjectConic Quadratic Programmingen_US
dc.subjectInterior Point Methodsen_US
dc.subjectNonparametric Regressionen_US
dc.subjectMultivariate Adaptive Regression Splinesen_US
dc.titleCMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimizationen_US
dc.titleCMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization
dc.typeArticleen_US

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