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E-raamat: Robust Optimization of Spline Models and Complex Regulatory Networks: Theory, Methods and Applications

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Robust Optimization of Spline Models and Complex Regulatory Networks: Theory, Methods and ApplicationsSuurem pilt
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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.

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.
1 Introduction
1(8)
1.1 Purpose of the Study
2(1)
1.2 The Significance of Uncertainty
3(1)
1.3 Robust Optimization
4(1)
1.4 Complex Multi-Modal Regulatory Networks
5(1)
1.5 Scope of the Book
6(3)
2 Mathematical Methods Used
9(26)
2.1 Optimization
9(9)
2.1.1 Robust Optimization
9(2)
2.1.2 Conic Optimization
11(4)
2.1.3 Robust Conic Optimization
15(1)
2.1.4 Multi-Objective Optimization
16(1)
2.1.5 Optimization Softwares
17(1)
2.2 Dynamical System of Complex Multi-Modal Regulatory Networks
18(3)
2.2.1 Time-Continuous Regulatory Networks
18(1)
2.2.2 Time-Discrete Regulatory Networks
19(2)
2.3 Inverse Problems and Parameter Estimation
21(14)
2.3.1 Least-Squares Estimation
21(2)
2.3.2 Regression and Classification
23(6)
2.3.3 Multivariate Adaptive Regression Splines
29(2)
2.3.4 Tikhonov Regularization
31(4)
3 New Robust Analytic Tools
35(24)
3.1 Robust (Conic) Multivariate Adaptive Regression Splines
35(16)
3.1.1 Introduction
35(1)
3.1.2 The Procedure
36(5)
3.1.3 Polyhedral Uncertainty and Robust Counterparts
41(2)
3.1.4 Robust Conic Quadratic Programming with Polyhedral Uncertainty
43(1)
3.1.5 Numerical Experience with RMARS in the Financial Economics
44(4)
3.1.6 Simulation Study for RMARS
48(3)
3.2 Robust (Conic) Generalized Partial Linear Models
51(8)
3.2.1 Introduction
51(1)
3.2.2 General Description of (C)GPLM
51(2)
3.2.3 Robustification of (C)GPLM
53(1)
3.2.4 Linear (Logit) Regression Model for the Linear Part
54(1)
3.2.5 R(C)MARS Method for the Nonlinear Part
55(1)
3.2.6 R(C)GPLM with Polyhedral Uncertainty
55(4)
4 Spline Regression Models for Complex Multi-Model Regulatory Networks
59(14)
4.1 Regression Problem for Regulatory Network with Spline Entries
61(2)
4.1.1 Introduction
61(1)
4.1.2 The Dynamical Procedure
62(1)
4.2 Numerical Experience on a Complex Multi-Model Regulatory Networks
63(8)
4.2.1 Data Description
63(2)
4.2.2 MARS Models
65(1)
4.2.3 CMARS Models
66(3)
4.2.4 Results and Comparison
69(2)
4.3 Simulation Study
71(2)
5 Robust Optimization in Spline Regression Models for Regulatory Networks Under Polyhedral Uncertainty
73(16)
5.1 Robustification of Regression for Regulatory Networks
73(8)
5.1.1 Polyhedral Uncertainty and Robust Counterpart for Regulatory Networks
79(1)
5.1.2 Robust Conic Quadratic Programming with Polyhedral Uncertainty
80(1)
5.2 Numerical Experience
81(8)
5.2.1 Developing RCMARS Models for Regulatory Networks
81(2)
5.2.2 Results
83(2)
5.2.3 Simulation Study and Comparison
85(4)
6 Real-World Application with Our Robust Tools
89(26)
6.1 A Real-World Application of RCMARS in the Financial Sector
89(9)
6.1.1 Introduction
89(1)
6.1.2 Data Description
89(2)
6.1.3 Obtaining Large Model from MARS Program
91(1)
6.1.4 Bootstraping
92(1)
6.1.5 Evaluating Accuracy and Complexity of PRSS Form
93(1)
6.1.6 Calculating Uncertainty Values for Input and Output Data under Polyhedral Uncertainty
94(1)
6.1.7 Receiving Weak RCMARS Models Using Combinatorial Approach
95(2)
6.1.8 Sensitivity to the Changes in the Confidence Interval Limits of RCMARS
97(1)
6.1.9 Results and Discussion
97(1)
6.2 A Real-World Application of RCMARS in the Energy Sector
98(3)
6.2.1 Dynamic Regression Approach
99(1)
6.2.2 CMARS
99(1)
6.2.3 RCMARS
100(1)
6.2.4 Results and Comparison
100(1)
6.3 A Real-World Application of RCMARS in the Environmental Sector
101(5)
6.3.1 Introduction
101(1)
6.3.2 Dataset and Its Preprocessing
102(1)
6.3.3 Criteria and Measures Used in Performance Evaluations
103(1)
6.3.4 Developing Precipitation Models
103(2)
6.3.5 Results and Discussion
105(1)
6.4 A Real-World Application with RCGPLM in the Financial Sector
106(9)
6.4.1 Introduction
106(1)
6.4.2 Data
107(2)
6.4.3 Application
109(2)
6.4.4 Application of the Model on the Testing Sample
111(1)
6.4.5 Results and Comparison
112(3)
7 Conclusion and Outlook
115(4)
A Coefficients and Performance of MARS-CMARS Models for TE Networks 119(4)
B Performance of R(C)MARS Models for TE Networks 123(4)
C Sensitivity and Performance of MARS for Forecasting of Precipitation 127(4)
D Prediction Performance Criteria and Related Measures 131(2)
References 133
Aye 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. 
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