CMARS: A new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization Regression 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. par 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.

References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Cheung, Ngaam J.; Xu, Zhen-Kai; Ding, Xue-Ming; Shen, Hong-Bin: Modeling nonlinear dynamic biological systems with human-readable fuzzy rules optimized by convergent heterogeneous particle swarm (2015)
  2. Kartal Koc, Elcin; Bozdogan, Hamparsum: Model selection in multivariate adaptive regression splines (MARS) using information complexity as the fitness function (2015)
  3. Yazıcı, Ceyda; Yerlikaya-Özkurt, Fatma; Batmaz, İnci: A computational approach to nonparametric regression: bootstrapping CMARS method (2015)
  4. Goldberg, Noam; Kim, Youngdae; Leyffer, Sven; Veselka, Thomas D.: Adaptively refined dynamic program for linear spline regression (2014)
  5. Koc, Elcin Kartal; Iyigun, Cem: Restructuring forward step of MARS algorithm using a new knot selection procedure based on a mapping approach (2014)
  6. Koc, Elcin Kartal; Iyigun, Cem; Batmaz, İnci; Weber, Gerhard-Wilhelm: Efficient adaptive regression spline algorithms based on mapping approach with a case study on finance (2014)
  7. Özmen, A.; Kropat, E.; Weber, G.-W.: Spline regression models for complex multi-modal regulatory networks (2014)
  8. Özmen, Ayşe; Weber, Gerhard-Wilhelm; Çavuşoğlu, Zehra; Defterli, Özlem: The new robust conic GPLM method with an application to finance: prediction of credit default (2013)
  9. Volkovich, Zeev; Barzily, Zeev; Weber, Gerhard-Wilhelm; Toledano-Kitai, Dvora; Avros, Renata: An application of the minimal spanning tree approach to the cluster stability problem (2012)
  10. Weber, Gerhard-Wilhelm; Batmaz, İNci; Köksal, Gülser; Taylan, Pakize; Yerlikaya-Özkurt, Fatma: CMARS: A new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization (2012)
  11. Weber, Gerhard-Wilhelm; Cavuşoğlu, Zehra; Özmen, Ayşe: Predicting default probabilities in emerging markets by new conic generalized partial linear models and their optimization (2012)
  12. Kropat, Erik; Weber, Gerhard-Wilhelm; Belen, Selma: Dynamical gene-environment networks under ellipsoidal uncertainty: set-theoretic regression analysis based on ellipsoidal OR (2011)
  13. Özmen, Ayşe; Weber, Gerhard Wilhelm; Batmaz, İnci; Kropat, Erik: RCMARS: Robustification of CMARS with different scenarios under polyhedral uncertainty set (2011)