Yazar "Yerlikaya-Ozkurt, Fatma" seçeneğine göre listele

Listeleniyor 1 - 3 / 3
  • [ X ]
    Öğe
    CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization
    (Taylor & Francis Ltd, 2012) Weber, Gerhard-Wilhelm; Batmaz, Inci; Koksal, Gulser; Taylan, Pakize; Yerlikaya-Ozkurt, Fatma
    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.
  • [ X ]
    Öğe
    A new outlier detection method based on convex optimization: application to diagnosis of Parkinson's disease
    (Taylor & Francis Ltd, 2021) Taylan, Pakize; Yerlikaya-Ozkurt, Fatma; Bilgic Ucak, Burcu; Weber, Gerhard-Wilhelm
    Neuroscience is a combination of different scientific disciplines which investigate the nervous system for understanding of the biological basis. Recently, applications to the diagnosis of neurodegenerative diseases like Parkinson's disease have become very promising by considering different statistical regression models. However, well-known statistical regression models may give misleading results for the diagnosis of the neurodegenerative diseases when experimental data contain outlier observations that lie an abnormal distance from the other observation. The main achievements of this study consist of a novel mathematics-supported approach beside statistical regression models to identify and treat the outlier observations without direct elimination for a great and emerging challenge in humankind, such as neurodegenerative diseases. By this approach, a new method named as CMTMSOM is proposed with the contributions of the powerful convex and continuous optimization techniques referred to as conic quadratic programing. This method, based on the mean-shift outlier regression model, is developed by combining robustness of M-estimation and stability of Tikhonov regularization. We apply our method and other parametric models on Parkinson telemonitoring dataset which is a real-world dataset in Neuroscience. Then, we compare these methods by using well-known method-free performance measures. The results indicate that the CMTMSOM method performs better than current parametric models.
  • [ X ]
    Öğe
    On the foundations of parameter estimation for generalized partial linear models with B-splines and continuous optimization
    (Pergamon-Elsevier Science Ltd, 2010) Taylan, Pakize; Weber, Gerhard-Wilhelm; Liu, Lian; Yerlikaya-Ozkurt, Fatma
    Generalized linear models are widely used in statistical techniques. As an extension, generalized partial linear models utilize semiparametric methods and augment the usual parametric terms with 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 the penalized maximum likelihood and the penalized iteratively reweighted least squares (P-IRLS) problem based on B-splines, which is attractive for nonparametric components. Then, we approach solving the P-IRLS problem using continuous optimization techniques. They have come to constitute an important complementary approach, alternative to the penalty methods, with flexibility for choosing the penalty parameter adaptively. In particular, we model and treat the constrained P-IRIS problem by using the elegant framework of conic quadratic programming. The method is illustrated using a small numerical example. (C) 2010 Elsevier Ltd. All rights reserved.