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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.
List of contents
Introduction.- Mathematical Methods Used.- New Robust Analytic Tools.- Spline Regression Models for Complex Multi-Model Regulatory Networks.- Robust Optimization in Spline Regression Models for Regulatory Networks Under Polyhedral Uncertainty.- Real-World Application with Our Robust Tools.- Conclusion and Outlook.
About the author
Ayşe Özmen has affiliation at Turkish Energy
Foundation(TENVA)and Institute of Applied Mathematics of Middle East Technical
University (METU), Ankara, Turkey. Her research is on OR, optimization, energy
modelling, renewable energy systems, network modelling, regulatory networks, data
mining. She received her Doctorate in Scientific Computing at Institute for
Applied Mathematics at METU.
Summary
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.
