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
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 Tikhonov regularization problem. Additionally, by modifying the forward step of MARS via mapping approach, a time efficient procedure has been introduced by S-FMARS. Inspiring from the advantages of MARS, CMARS and S-FMARS, two hybrid methods are proposed in this study, aiming to produce time efficient DM tools without degrading their performances especially for large datasets. The resulting methods, called SMARS and SCMARS, are tested in terms of several performance criteria such as accuracy, complexity, stability and robustness via simulated and real life datasets. As a DM application, the hybrid methods are also applied to an important field of finance for predicting interest rates offered by a Turkish bank to its customers. The results show that the proposed hybrid methods, being the most time efficient with competing performances, can be considered as powerful choices particularly for large datasets.


Batmaz, İnci; Kartal-Koc, Elcin; Köksal, Gülser (2010-02-04)
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 nonline...
A new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimization
TAYLAN, PAKİZE; Weber, Gerhard Wilhelm; Ozkurt, Fatma Yerlikaya (2010-12-01)
This paper introduces a model-based approach to the important data mining tool Multivariate adaptive regression splines (MARS), which has originally been organized in a more model-free way. Indeed, MARS denotes a modern methodology from statistical learning which is important in both classification and regression, with an increasing number of applications in many areas of science, economy and technology. It is very useful for high-dimensional problems and shows a great promise for fitting nonlinear multivar...
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 ...
Continuous optimization applied in MARS for modern applications in finance, science and technology
Taylan, Pakize; Weber, Gerhard Wilhelm; Yerlikaya, Fatma (2008-05-23)
Multivariate adaptive regression spline (MARS) denotes a tool from statistics, important in classification and regression, with applicability in many areas of finance, science and technology. It is very useful in high dimensions and shows a great promise for fitting nonlinear multivariate functions. The MARS algorithm for estimating the model function consists of two subalgorithms. We propose not to use the second one (backward stepwise algorithm), but we construct a penalized residual sum of squares for a ...
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...
Citation Formats
E. K. Koc, C. İyigün, İ. Batmaz, and G.-W. Weber, “Efficient adaptive regression spline algorithms based on mapping approach with a case study on finance,” JOURNAL OF GLOBAL OPTIMIZATION, pp. 103–120, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32961.