A computational approach to nonparametric regression: bootstrapping CMARS method

Download

index.pdf

Date

2015-10-01

Author

Yazici, Ceyda
Yerlikaya-Ozkurt, Fatma
Batmaz, İnci

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

362
views

0
downloads

Bootstrapping is a computer-intensive statistical method which treats the data set as a population and draws samples from it with replacement. This resampling method has wide application areas especially in mathematically intractable problems. In this study, it is used to obtain the empirical distributions of the parameters to determine whether they are statistically significant or not in a special case of nonparametric regression, conic multivariate adaptive regression splines (CMARS), a statistical machine learning algorithm. CMARS is the modified version of the well-known nonparametric regression model, multivariate adaptive regression splines (MARS), which uses conic quadratic optimization. CMARS is at least as complex as MARS even though it performs better with respect to several criteria. To achieve a better performance of CMARS with a less complex model, three different bootstrapping regression methods, namely, random-X, fixed-X and wild bootstrap are applied on four data sets with different size and scale. Then, the performances of the models are compared using various criteria including accuracy, precision, complexity, stability, robustness and computational efficiency. The results imply that bootstrap methods give more precise parameter estimates although they are computationally inefficient and that among all, random-X resampling produces better models, particularly for medium size and scale data sets.

Subject Keywords

Machine learning, Wild bootstrap, Random-X resampling, Fixed-X resampling, Conic multivariate adaptive regression splines, Bootstrapping regression

URI

https://hdl.handle.net/11511/40591

Journal

MACHINE LEARNING

DOI

https://doi.org/10.1007/s10994-015-5502-3

Collections

Department of Statistics, Article

Suggestions

OpenMETU
Core

A computational approach to nonparametric regression: bootstrapping cmars method Yazıcı, Ceyda; Batmaz, İnci; Department of Statistics (2011) Bootstrapping is a resampling technique which treats the original data set as a population and draws samples from it with replacement. This technique is widely used, especially, in mathematically intractable problems. In this study, it is used to obtain the empirical distributions of the parameters to determine whether they are statistically significant or not in a special case of nonparametric regression, Conic Multivariate Adaptive Regression Splines (CMARS). Here, the CMARS method, which uses conic quadr...
A Methodology to Implement Box-Cox Transformation When No Covariate is Available Dag, Osman; Asar, Ozgur; İlk Dağ, Özlem (2014-01-01) Box-Cox transformation is one of the most commonly used methodologies when data do not follow normal distribution. However, its use is restricted since it usually requires the availability of covariates. In this article, the use of a non-informative auxiliary variable is proposed for the implementation of Box-Cox transformation. Simulation studies are conducted to illustrate that the proposed approach is successful in attaining normality under different sample sizes and most of the distributions and in esti...
A Bayesian Approach to Learning Scoring Systems Ertekin Bolelli, Şeyda (2015-12-01) We present a Bayesian method for building scoring systems, which are linear models with coefficients that have very few significant digits. Usually the construction of scoring systems involve manual efforthumans invent the full scoring system without using data, or they choose how logistic regression coefficients should be scaled and rounded to produce a scoring system. These kinds of heuristics lead to suboptimal solutions. Our approach is different in that humans need only specify the prior over what the ...
An fMRI segmentation method under markov random fields for brain decoding Aksan, Emre; Yarman Vural, Fatoş Tunay; Department of Computer Engineering (2015) In this study, a specially tailored segmentation method for partitioning the fMRI data into a set of "homogenous" regions with respect to a predefined cost function is proposed. The proposed method, referred as f-MRF, employs univariate and multivariate fMRI data analysis techniques under Markov Random Fields to estimate the segments by resolving a mixture density. The univariate approach helps identifying activation pattern of a voxel independently from other voxels. In order to capture local interactions ...
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...

Citation Formats

C. Yazici, F. Yerlikaya-Ozkurt, and İ. Batmaz, “A computational approach to nonparametric regression: bootstrapping CMARS method,” MACHINE LEARNING, pp. 211–230, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40591.