Robust Optimization of Spline Models and Complex Regulatory Networks

This book introduces methods of robust optimization in multivariate
adaptive regression splines (MARS) and Conic MARS in order to handle
uncertainty and non-linearity. The proposed techniques are implemented and
explained in two-model regulatory systems that can be found in the financial
sector and in the contexts of banking, environmental protection, system biology
and medicine. The book provides necessary
background information on multi-model regulatory networks, optimization
and 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 and
interprets (C)MARS results based on different datasets for the implementation.
It explains robust optimization in these models in terms of both the theory and
methodology. In this context it studies R(C)MARS results with different
uncertainty scenarios for a numerical example. Lastly, the book demonstrates
the implementation of the method in a number of applications from the
financial, energy, and environmental sectors, and provides an outlook on future
research.