Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization
Date
2012-01-01
Author
Weber, Gerhard-Wilhelm
Batmaz, İnci
Köksal, Gülser
Taylan, Pakize
Yerlikaya-Ozkurt, Fatma
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
363
views
0
downloads
Cite This
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. 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.
Subject Keywords
Conic quadratic programming
,
Tikhonov regularization
,
Multivariate adaptive regression splines
,
Nonparametric regression
,
Interior point methods
URI
https://hdl.handle.net/11511/46678
Journal
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
DOI
https://doi.org/10.1080/17415977.2011.624770
Collections
Department of Statistics, Article
Suggestions
OpenMETU
Core
EVALUATING THE CMARS PERFORMANCE FOR MODELING NONLINEARITIES
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...
Parameter estimation in generalized partial linear models with conic quadratic programming
Çelik, Gül; Weber, Gerhard Wilhelm; Department of Scientific Computing (2010)
In statistics, regression analysis is a technique, used to understand and model the relationship between a dependent variable and one or more independent variables. Multiple Adaptive Regression Spline (MARS) is a form of regression analysis. It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models non-linearities and interactions. MARS is very important in both classification and regression, with an increasing number of applications in many areas...
Analyses of Two Different Regression Models and Bootstrapping
Gökalp Yavuz, Fulya (Springer, Berlin, Heidelberg, 2011-09-02)
Regression methods are used to explain the relationship between a single response variable and one or more explanatory variables. Graphical methods are generally the first step and are used to identify models that can be explored to describe the relationship. Although linear models are frequently used and they are user friendly, many important associations are not linear and require considerably more analytical effort. This study is focused on such nonlinear models. To perform statistical inference in this ...
ROBUST CONIC GENERALIZED PARTIAL LINEAR MODELS USING RCMARS METHOD - A ROBUSTIFICATION OF CGPLM
Ozmen, Ayse; Weber, Gerhard Wilhelm (2012-08-08)
GPLM is a combination of two different regression models each of which is used to apply on different parts of the data set. It is also adequate to high dimensional, non-normal and nonlinear data sets having the flexibility to reflect all anomalies effectively. In our previous study, Conic GPLM (CGPLM) was introduced using CMARS and Logistic Regression. According to a comparison with CMARS, CGPLM gives better results. In this study, we include the existence of uncertainty in the future scenarios into CMARS a...
ON FOUNDATIONS OF PARAMETER ESTIMATION FOR GENERALIZED PARTIAL LINEAR MODELS WITH B-SPLINES AND CONTINUOUS OPTIMIZATION
TAYLAN, PAKİZE; Weber, Gerhard Wilhelm; Liu, Lian (2010-02-04)
Generalized linear models are widely-used statistical techniques. As an extension, generalized partial linear models utilize semiparametric methods and augment the usual parametric terms by a single nonparametric component of a continuous covariate. In this paper, after a short introduction, we present our model in the generalized additive context with a focus on penalized maximum likelihood and on the penalized iteratively reweighted least squares (P-IRLS) problem based on B-splines which is attractive for...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
G.-W. Weber, İ. Batmaz, G. Köksal, P. Taylan, and F. Yerlikaya-Ozkurt, “CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization,”
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
, pp. 371–400, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46678.