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.
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