(C)MARS and R(C)MARS with Comparison Studies
Tarih: -
Konum: B141
Speaker: Dr. Ayşe Özmen
(C)MARS and R(C)MARS with Comparison Studies
Multivariate Adaptive Regression Spline (MARS) is a modern methodology of data mining, statistical learning, and estimation theory that is essential in both regression and classification. In recent years, MARS is applied in various areas of science, technology, finance, and engineering. It is a form of flexible non-parametric regression analysis capable of modeling complex data. Conic MARS (CMARS) is an alternative method to a well-known regression tool MARS from data mining and estimation theory. In CMARS method, a Penalized Residual Sum of Squares (PRSS) is employed for MARS as a Tikhonov Regularization (TR) problem. This two-objective optimization problem is treated using the continuous optimization technique called Conic Quadratic Programming (CQP). However, for MARS and CMARS, it is supposed that the input data are known exactly and equal to some nominal values to construct a model. In fact, both output and input data include noise in real life. As a result, in inverse problems of modeling, solutions to the optimization problems involved in (C)MARS can represent a remarkable sensitivity with respect to perturbations in the parameters which base on the data, and a computed solution can be highly infeasible, suboptimal, or both. Under this motivation, we have included the existence of uncertainty into (C)MARS and robustified it through robust optimization which is proposed to cope with data and, hence, parametric uncertainty. We have represented Robust (C)MARS (R(C)MARS) under polyhedral uncertainty. By using robustification in (C)MARS, we try to reduce the estimation variance. While in prior studies due to the large complexity of the underlying model we applied what is called a weak robustification, now we suggest exploiting a geometrical and combinatorial approach to allow for a more complete robustification, by formulating R(C)MARS under Cross-Polytope Uncertainty. In this presentation, firstly, we obtain MARS and CMARS models for natural gas demand forecasting in Ankara and compare them with LR, TR, ANN, and LASSO (in linear and nonlinear cases) models. Then, we compare the performance of the weak RCMARS model with the performance of MARS and CMARS on rainfall data. Finally, we present a more robust model using cross-polytope and demonstrate the performance of RMARS with the application of Natural Gas consumption prediction.
Keywords: Robust Optimization; Robustness and sensitivity analysis; Machine Learning; Mathematical Programming
Bio of the speaker: Dr. Özmen earned her B.S. degrees in Industrial Engineering and Mathematics and Computer Science (as a double major) from Çankaya University in 2006. She received her M.S. and Ph.D. degrees in Scientific Computing at the Institute of Applied Mathematics from Middle East Technical University (METU) in 2010 and 2015, respectively. At the University of Calgary, Canada, she has worked as a Post-doctoral Scholar in the Department of Mathematics and Statistics for 1.5 years. Then, she has worked as an Energy Efficiency Specialist at SIS Energy-Geothermal Energy Plant in Manisa for 1 year. Her research is on Operational Research, Optimization, Data Science, Statistical Learning, Machine Learning, and Mathematical Modeling and Programming, Energy Modeling, Network Modelling, and Regulatory Networks. Dr. Özmen has participated in many research projects from different areas and (co-)authored lots of special issues and articles.