Journal ArticleDOI
CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization
TLDR
In this article, the authors used a penalized residual sum of squares for MARS as a Tikhonov regularization problem, and treated this with continuous optimization technique, in particular, the framework of conic quadratic programming.Abstract:
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 algo...read more
Citations
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Journal ArticleDOI
RCMARS: Robustification of CMARS with different scenarios under polyhedral uncertainty set
TL;DR: This study presents the new robust CMARS (RCMARS) in theory and method and results with different uncertainty scenarios for the authors' numerical example, and refine the CMARS algorithm by a robust optimization technique proposed to cope with data uncertainty.
Journal ArticleDOI
Long-term load forecasting: models based on MARS, ANN and LR methods
TL;DR: This paper suggests three models based on multivariate adaptive regression splines (MARS), artificial neural network (ANN) and linear regression (LR) methods to model electrical load overall in the Turkish electricity distribution network, and shows that MARS model gives more accurate and stable results than ANN and LR models.
Journal ArticleDOI
Retrieval of fractional snow covered area from MODIS data by multivariate adaptive regression splines
TL;DR: In this paper, a novel approach to estimate fractional snow cover (FSC) from MODIS data in a complex and heterogeneous Alpine terrain is represented by using a state-of-the-art nonparametric spline regression method, namely multivariate adaptive regression splines (MARS).
Journal ArticleDOI
Performance models for hot mix asphalt pavements in urban roads
Ufuk Kırbaş,Mustafa Karaşahin +1 more
TL;DR: In this paper, three different deterioration models have been developed that can predict the future performance of pavements in urban HMA paved roads, including deterministic regression analysis, multivariate adaptive regression splines (MARS) and artificial neural networks (ANN).
Journal ArticleDOI
RMARS: Robustification of multivariate adaptive regression spline under polyhedral uncertainty
Ayşe Özmen,Gerhard-Wilhelm Weber +1 more
TL;DR: This work represents the new Robust MARS (RMARS) in theory and method and applies RMARS on financial market data to indicate that models from RMARS have much less variability in parameter estimates and in accuracy measures, to the cost of just a slightly lower accuracy than MARS.
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