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 31 articles , 1 standard article )

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  1. Bülbül, Gül Bahar; Purutçuoglu, Vilda: Novel model selection criteria for LMARS: MARS designed for biological networks (2021)
  2. Miller, A.; Mulholland, A. J.; Tant, K. M. M.; Pierce, S. G.; Hughes, B.; Forbes, A. B.: Reconstruction of refractive index maps using photogrammetry (2021)
  3. Romanovski, M.: A reconstruction of object properties with significant uncertainties (2021)
  4. Taylan, Pakize; Yerlikaya-Özkurt, Fatma; Bilgiç Uçak, Burcu; Weber, Gerhard-Wilhelm: A new outlier detection method based on convex optimization: application to diagnosis of Parkinson’s disease (2021)
  5. Ağraz, Melih; Purutçuoğlu, Vilda: Extended Lasso-type MARS (LMARS) model in the description of biological network (2019)
  6. Černý, Michal: Narrow big data in a stream: computational limitations and regression (2019)
  7. Nalcaci, Gamze; Özmen, Ayse; Weber, Gerhard Wilhelm: Long-term load forecasting: models based on MARS, ANN and LR methods (2019)
  8. Sahiner, Ahmet; Yilmaz, Nurullah; Kapusuz, Gulden: A novel modeling and smoothing technique in global optimization (2019)
  9. Yilmaz, Nurullah; Sahiner, Ahmet: New smoothing approximations to piecewise smooth functions and applications (2019)
  10. Liu, Yanqing; Tao, Jiyuan; Zhang, Huan; Xiu, Xianchao; Kong, Lingchen: Fused Lasso penalized least absolute deviation estimator for high dimensional linear regression (2018)
  11. Onak, Onder Nazim; Dogrusoz, Yesim Serinagaoglu; Weber, Gerhard Wilhelm: Effects of a priori parameter selection in minimum relative entropy method on inverse electrocardiography problem (2018)
  12. Ayyıldız, Ezgi; Ağraz, Melih; Purutçuoğlu, Vilda: MARS as an alternative approach of Gaussian graphical model for biochemical networks (2017)
  13. Çevik, Alper; Weber, Gerhard-Wilhelm; Eyüboğlu, B. Murat; Oğuz, Kader Karlı: Voxel-MARS: a method for early detection of Alzheimer’s disease by classification of structural brain MRI (2017)
  14. Li, Zhi; Tan, De-qing: Two-stage dynamic pricing and advertising strategies for online video services (2017)
  15. Bozağaç, Doruk; Batmaz, İnci; Oğuztüzün, Halit: Dynamic simulation metamodeling using Mars: a case of radar simulation (2016)
  16. 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)
  17. Kartal Koc, Elcin; Bozdogan, Hamparsum: Model selection in multivariate adaptive regression splines (MARS) using information complexity as the fitness function (2015)
  18. Yazıcı, Ceyda; Yerlikaya-Özkurt, Fatma; Batmaz, İnci: A computational approach to nonparametric regression: bootstrapping CMARS method (2015)
  19. Goldberg, Noam; Kim, Youngdae; Leyffer, Sven; Veselka, Thomas D.: Adaptively refined dynamic program for linear spline regression (2014)
  20. Koc, Elcin Kartal; Iyigun, Cem: Restructuring forward step of MARS algorithm using a new knot selection procedure based on a mapping approach (2014)

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