Robust Optimization of Spline Models and Complex Regulatory Networks

This book introduces methods of robust optimization in multivariateadaptive regression splines (MARS) and Conic MARS in order to handleuncertainty and non-linearity. The proposed techniques are implemented andexplained in two-model regulatory systems that can be found in the financialsector and in the contexts of banking, environmental protection, system biologyand medicine. The book provides necessarybackground information on multi-model regulatory networks, optimizationand regression. It presents the theory of and approaches to robust (conic)multivariate adaptive regression splines - R(C)MARS – and robust (conic)generalized partial linear models – R(C)GPLM – under polyhedral uncertainty. Further,it introduces spline regression models for multi-model regulatory networks andinterprets (C)MARS results based on different datasets for the implementation.It explains robust optimization in these models in terms of both the theory andmethodology. In this context it studies R(C)MARS results with differentuncertainty scenarios for a numerical example. Lastly, the book demonstratesthe implementation of the method in a number of applications from thefinancial, energy, and environmental sectors, and provides an outlook on futureresearch.