CMARS: A New Contribution to Nonparametric Regression with MARS

This book is originated from my MSc thesis supervised by Prof. Dr. Gerhard-Wilhelm Weber at Institute of Applied Mathematics (IAM), and Assoc. Prof. Dr. İnci Batmaz at Department of Statistics, Middle East Technical University (METU), Turkey. Multivariate adaptive regression splines (MARS) denotes a modern methodology from statistical learning which is very important in both classification and regression, with an increasing number of applications in many areas of science, economy and technology. CMARS which is developed at IAM, METU, as an alternative approach to the well-known data mining tool MARS. CMARS is based on a penalized residual sum of squares for MARS as a Tikhonov regularization problem. It treats this problem by a continuous optimization technique called Conic Quadratic Programming. The boundaries of this optimization problem are determined by the multiobjective optimization approach which provides us many alternative solutions. Based on these theoretical and algorithmical studies, this work also contains applications on the data for the quality control. By these applications, MARS and our new method CMARS are compared.