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Article Citation - WoS: 2A new approach to adaptive spline threshold autoregression by using Tikhonov regularization and continuous optimization(Taru Publications, 2019) Yalaz, S.; Taylan, P.; Ozkurt, F. YerlikayaIn this study adaptive spline threshold autoregression and conic quadratic programming is used to develope conic adaptive spline threshold autoregression. With the introduced approach the second stepwise algorithm of adaptive spline threshold autoregression model turned to the Tikhonov regularization problem which was transformed into conic quadratic programming problem. The aim is to attain an optimum solution chosen in many solutions obtained by determining the bounds of the optimization problem using multiobjective optimization approach. Furthermore, in application part we used two different data set to compare performances of linear regression, adaptive spline threshold autoregression and conic adaptive spline threshold autoregression approaches.Article Citation - WoS: 3Citation - Scopus: 4Cmars: a Powerful Predictive Data Mining Package in R(Elsevier, 2023) Yerlikaya-oezkurt, Fatma; Yazici, Ceyda; Batmaz, InciConic Multivariate Adaptive Regression Splines (CMARS) is a very successful method for modeling nonlinear structures in high-dimensional data. It is based on MARS algorithm and utilizes Tikhonov regularization and Conic Quadratic Optimization (CQO). In this paper, the open-source R package, cmaRs, built to construct CMARS models for prediction and binary classification is presented with illustrative applications. Also, the CMARS algorithm is provided in both pseudo and R code. Note here that cmaRs package provides a good example for a challenging implementation of CQO based on MOSEK solver in R environment by linking R MOSEK through the package Rmosek.Article Citation - WoS: 9Citation - Scopus: 8New Computational Methods for Classification Problems in the Existence of Outliers Based on Conic Quadratic Optimization(Taylor & Francis inc, 2020) Yerlikaya-Ozkurt, Fatma; Taylan, PakizeMost of the statistical research involves classification which is a procedure utilized to establish prediction models to set apart and classify new observations in the dataset from every fields of science, technology, and economics. However, these models may give misclassification results when dataset contains outliers (extreme data points). Therefore, we dealt with outliers in classification problem: firstly, by combining robustness of mean-shift outlier model and then stability of Tikhonov regularization based on continuous optimization method called Conic Quadratic Programming. These new methodologies are performed on classification dataset within the existence of outliers, and the results are compared with parametric model by using well-known performance measures.
