Batmaz, İnci
Kartal-Koc, Elcin
Köksal, Gülser
Multivariate Adaptive Regression Splines (MARS) is a very popular nonparametric regression method particularly useful for modeling nonlinear relationships that may exist among the variables. Recently, we developed CMARS method as an alternative to backward stepwise part of the MARS algorithm. Comparative studies have indicated that CMARS performs better than MARS for modeling nonlinear relationships. In those studies, however, only main and two-factor interaction effects were sufficient to model the nonlinearity between the variables in the data sets. In this study, therefore, we aim at evaluating the model performances when there is a need for representing higher-order interaction effects in a nonlinear model. Results based on the comparison studies show that CMARS method performs better than MARS method according to most of the performance measures.


CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization
Weber, Gerhard-Wilhelm; Batmaz, İnci; Köksal, Gülser; Taylan, Pakize; Yerlikaya-Ozkurt, Fatma (2012-01-01)
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 an...
Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method
Yerlikaya-Ozkurt, F.; Vardar Acar, Ceren; Yolcu-Okur, Y.; Weber, G. -W. (2014-03-15)
In this study, we develop an alternative method for estimating the Hurst parameter using the conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solutions of stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm). Our approach is superior to others in that it not only estimates the Hurst parameter but also finds spline parameters of the stochastic process in an adaptive way. We examine the performance of our estimations using simulated tes...
Restructuring forward step of MARS algorithm using a new knot selection procedure based on a mapping approach
Koc, Elcin Kartal; İyigün, Cem (2014-09-01)
In high dimensional data modeling, Multivariate Adaptive Regression Splines (MARS) is a popular nonparametric regression technique used to define the nonlinear relationship between a response variable and the predictors with the help of splines. MARS uses piecewise linear functions for local fit and apply an adaptive procedure to select the number and location of breaking points (called knots). The function estimation is basically generated via a two-stepwise procedure: forward selection and backward elimin...
Efficient adaptive regression spline algorithms based on mapping approach with a case study on finance
Koc, Elcin Kartal; İyigün, Cem; Batmaz, İnci; Weber, Gerhard-Wilhelm (2014-09-01)
Multivariate adaptive regression splines (MARS) has become a popular data mining (DM) tool due to its flexible model building strategy for high dimensional data. Compared to well-known others, it performs better in many areas such as finance, informatics, technology and science. Many studies have been conducted on improving its performance. For this purpose, an alternative backward stepwise algorithm is proposed through Conic-MARS (CMARS) method which uses a penalized residual sum of squares for MARS as a T...
Refinements, extensions and modern applications of conic multivariate adaptive regression splines
Yerlikaya Özkurt, Fatma; Weber, Gerhard Wilhelm; Department of Scientific Computing (2013)
Conic Multivariate Adaptive Regression Splines (CMARS) which has been developed at the Institute of Applied Mathematics, METU, as an alternative approach to the well-known data mining tool Multivariate Adaptive Regression Splines (MARS). CMARS is based on given data and a penalized residual sum of squares for MARS, interpreted as a Tikhonov Regularization problem. CMARS treats this problem by a continuous optimization technique called Conic Quadratic Programming (CQP). This doctoral thesis adapts the CMARS ...
Citation Formats
İ. Batmaz, E. Kartal-Koc, and G. Köksal, “EVALUATING THE CMARS PERFORMANCE FOR MODELING NONLINEARITIES,” 2010, vol. 1239, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47034.