Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Introduction

  • Chapter
  • First Online:
Robust Optimization of Spline Models and Complex Regulatory Networks

Part of the book series: Contributions to Management Science ((MANAGEMENT SC.))

  • 607 Accesses

Abstract

Multivariate adaptive regression splines (MARS) (J.H. Friedman, Multivariate adaptive regression splines, The Annals of Statistics, 19(1), pp. 1–141, 1991) is a form of non-parametric regression analysis for building high-dimensional and nonlinear multivariate functions and applied in many fields of science, engineering, technology, finance and control design in recent years. It is a modern methodology of statistical learning, data mining and mathematical estimation theory which is important in both regression and classification, and develops an multiplicative-additive model in a two-stage process, namely, forward and backward, without specific assumptions about the underlying functional relationship between the variables (T. Hastie, R. Tibshirani and J. H. Friedman, The Element of Statistical Learning, Springer Verlag, New York, 2001; M. Kriner, Survival Analysis with Multivariate adaptive Regression Splines, Dissertation, LMU Munchen: Faculty of Mathematics, Computer Science and Statistics, 2007). Continuing on the success of MARS in modeling real-life problems, as an alternative to MARS, Conic MARS (CMARS) (P. Taylan, G.-W. Weber and A. Beck, New approaches to regression by generalized additive models and continuous optimization for modern applications in finance, science and technology, Journal Optimization 56, 5–6, pp. 1–24, 2007; G.-W. Weber, İ. Batmaz, G. Köksal, P. Taylan and F. Yerlikaya, CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization, IPSE 20 (3), pp. 371–400, 2012) was developed for the backward part of the MARS algorithm in a previous study. For this approach, a Penalized Residual Sum of Squares (PRSS) is employed for MARS as a Tikhonov regularization (TR) problem (R. C. Aster, B. Borchers and C. Thurber, Parameter Estimation and Inverse Problems, Academic Press, 2004), and then, it is treated with a continuous optimization technique, namely, Conic Quadratic Programming (CQP) (A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MPR-SIAM Series on Optimization, SIAM, Philadelphia, 2001).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

eBook
USD 12.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. R. C. Aster, B. Borchers and C. Thurber, Parameter Estimation and Inverse Problems, Academic Press, 2004.

    Google Scholar 

  2. A. Ben-Tal and A. Nemirovski, Robust convex optimization, Mathematics of Operations Research, 23, pp. 769–805, 1998.

    Article  Google Scholar 

  3. A. Ben-Tal and A. Nemirovski, Robust solutions to uncertain linear programs, Operations Research Letters, 25(1), pp. 1–13, 1999.

    Article  Google Scholar 

  4. A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MPR-SIAM Series on Optimization, SIAM, Philadelphia, 2001.

    Book  Google Scholar 

  5. A. Ben-Tal and A. Nemirovski, Robust optimization - methodology and applications, Mathematical Programming, 92(3), pp. 453–480, 2002.

    Article  Google Scholar 

  6. A. Ben-Tal, L. El-Ghaoui, and A. Nemirovski, Robust Optimization, Princeton University Press, 2009.

    Book  Google Scholar 

  7. D.P. Bertsekas, Dynamic Programming and Optimal Control, Athena Scientific, Belmont, Mass., 1995.

    Google Scholar 

  8. D. Bertsimas, M. Sim, Price of Robustness, Oper. Res. 52(1), pp. 35–53, 2004.

    Article  Google Scholar 

  9. D. Bertsimas, D.B. Brown, C. Caramanis, Theory and applications of Robust Optimization, Technical Report, University of Texas, Austin, TX, USA, 2007.

    Google Scholar 

  10. O. Boni, Robust Solutions of Conic Quadratic Problems, PhD Thesis, Technion, Israeli Institute of Technology, IEM faculty, 2007.

    Google Scholar 

  11. B. Bower. Banks err by confusing risk, uncertainty, Science News, 182(10), pp. 13, 2012.

    Google Scholar 

  12. E. Borenstein and M.W. Feldman, Topological signatures of species interactions in metabolic networks, Journal of Computational Biology, 16(2), pp.191–200, 2009.

    Article  Google Scholar 

  13. A. Charnes and W.W. Cooper, Chance constrained programming, Management Science, 6, pp. 73–89, 1959.

    Article  Google Scholar 

  14. T. Chen, H. L. He and G. M. Church, Modeling gene expression with differential equations, Pacific Symposium on Biocomputing, 4, pp. 29–40, 1999.

    Google Scholar 

  15. L. El-Ghaoui and H. Lebret, Robust solutions to least-square problems to uncertain data matrices, SIAM Journal on Matrix Analysis and Applications, 18, pp. 1035–1064, 1997.

    Article  Google Scholar 

  16. L. El-Ghaoui, F. Oustry and H. Lebret, Robust solutions to uncertain semidefinite programs, SIAM Journal on Optimization 9, pp. 33–52, 1998.

    Article  Google Scholar 

  17. I. Elishakoff, Whys and Hows in Uncertainty Modelling, Probability, Fuzziness and Anti-Optimization, 1999.

    Book  Google Scholar 

  18. S.V. Emmerik, Risk, uncertainty and the financial crisis – Reflexivity in Finance, January 20, 2009. Page available at: http://reflexivityfinance.blogspot.com/2009/01/risk-uncertainty-and-financial-crisis.html.

  19. F.J. Fabozzi, P.N. Kolm, D.A. Pachamanova and S.M. Focardi, Robust Portfolio Optimization and Management, Willey Finance, 2007.

    Google Scholar 

  20. J.A. Filar and A. Haurie, Uncertainty and Enviromental Decision Making, Springer, 2010.

    Book  Google Scholar 

  21. J.H. Friedman, Multivariate adaptive regression splines, The Annals of Statistics, 19(1), pp. 1–141, 1991.

    Article  Google Scholar 

  22. J. Gebert, M. Lätsch, S.W. Pickl, G.-W. Weber and R. Wünschiers: An algorithm to analyze stability of gene-expression pattern, In M. Anthony, E. Boros, P.L. Hammer, and A. Kogan (guest eds.), special issue Discrete Mathematics and Data Mining II of Discrete Applied Mathematics, 154(7), pp. 1140–1156, 2006.

    Google Scholar 

  23. G. Gigerenzer, Cognitive foundations of risk judgments, 7th DFG-NSF conference -Reckoning with the risk of catastrophe, Washington, D.C., October 4, 2012, abstract available at: http://dfg-nsf2012.mit.edu/wp-content/uploads/2012/09/Conference-brochure.pdf.

  24. A. Gökmen, S. Kayalgil, G.-W. Weber, I. Gökmen, M. Ecevit, A. Sürmeli, T. Bali, Y. Ecevit, H. Gökmen and D.J. DeTombe, Balaban Valley Project: Improving the quality of life in rural area in Turkey. International Scientific Journal of Methods and Models Complexity, 7(1), 2004.

    Google Scholar 

  25. J.R. Harris, W. Nystad and P. Magnus, Using genes and environments to define asthma and related phenotypes: applications to multivariate data. Clinical and Experimental Allergy, 28(1), pp. 43–45, 1998.

    Article  Google Scholar 

  26. T. Hastie, R. Tibshirani and J. H. Friedman, The Element of Statistical Learning, Springer Verlag, New York, 2001.

    Book  Google Scholar 

  27. M.D. Hoon, S. Imoto, K. Kobayashi, N. Ogasawara and S. Miyano, Inferring gene regulatory networks from time-ordered gene expression data of Bacillus Subtilis using differential equations, Pacific Symposium on Biocomputing, 8, pp. 17–28, 2003.

    Google Scholar 

  28. H.D. Jong, Modeling and simulation of genetic regulatory systems: a literature review, Journal of Computational Biology, 9, pp. 103–129, 2002.

    Google Scholar 

  29. A. Kibzun, Y. Kan, Stochastic Programming Problems with Probability and Quantile Functions, Wiley, 1996.

    Google Scholar 

  30. W. Krabs and S. Pickl, A game-theoretic treatment of a time-discrete emission reduction model, International Game Theory Review, (6)1, pp. 21–34, 2004.

    Google Scholar 

  31. M. Kriner, Survival Analysis with Multivariate adaptive Regression Splines, Dissertation, LMU Munchen: Faculty of Mathematics, Computer Science and Statistics, 2007.

    Google Scholar 

  32. E. Kropat, S. Pickl and A.Rössler, G. W. Weber, On theoretical and practical relations between discrete optimization and nonlinear optimization, Special issue Colloquy Optimization Structure and Stability of Dynamical Systems (at the occasion of the colloquy with the same name, Cologne, October 2000) of Journal of Computational Technologies, 7, pp. 27–62, 2002.

    Google Scholar 

  33. E. Kropat and G.-W. Weber, Robust regression analysis for gene-environment and eco-finance networks under polyhedral and ellipsoidal uncertainty, preprint 2 at Institute of Applied Mathematics, METU, submitted to Optimization Methods and Software, 2010.

    Google Scholar 

  34. E. Kropat, G.-W. Weber and J.-J. Rückmann, Regression analysis for clusters in gene-environment networks based on ellipsoidal calculus and optimization, in the special issue in honour of Professor Alexander Rubinov of Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications & Algorithms 17, 5, pp. 639–657, 2010.

    Google Scholar 

  35. E. Kropat, G.-W. Weber and B. Akteke-Öztürk, Eco-Finance networks under uncertainty. Proceedings of the International Conference on Engineering Optimization (CD), Engineering Optimization Rio de Janeiro, Brazil, ISBN 978857650156-5, 2008.

    Google Scholar 

  36. E. Kropat, G.-W. Weber and C.S. Pedamallu, Regulatory networks under ellipsoidal uncertainty – Data Analysis and Prediction by Optimization theory and dynamical systems, in the book on Data Mining: Foundations and Intelligent Paradigms, 24, pp. 27–56, Springer-Verlag, Berlin, Heidelberg, 2012.

    Google Scholar 

  37. Kyoto (1997), Kyoto Contract, Page available at http://www.unfccc.org/resource/convkp.html

  38. Y.F. Li, S. Venkatesh and D. Li, Modeling global emissions and residues of pesticides, Environmental Modeling and Assessment, 9, pp. 237–243, 2004.

    Article  Google Scholar 

  39. A. Özmen, Robust Conic Quadratic Programming Applied to Quality Improvement- A Robustification of CMARS, Ms. Thesis, METU, Ankara, Turkey, 2010.

    Google Scholar 

  40. A. Özmen, G.-W. Weber, İ. Batmaz, and E. Kropat, RCMARS: Robustification of CMARS with Different Scenarios under Polyhedral Uncertainty Set, Communications in Nonlinear Science and Numerical Simulation, 16 (12), pp. 4780–4787, 2011.

    Article  Google Scholar 

  41. A. Özmen and G.-W. Weber, Robust conic generalized partial linear models using RCMARS method, AIP Conference Proceeding 1499, pp. 337–343, 2012.

    Article  Google Scholar 

  42. A. Özmen, G.-W. Weber and E. Kropat, Robustification of conic generalized partial linear models under polyhedral uncertainty, International IFNA-ANS scientific Journal “Problems of Nonlinear Analysis in Engineering Systems”, 2(38), 18, pp. 104–113, 2012.

    Google Scholar 

  43. A. Özmen, G.-W. Weber and A. Karimov, A new robust optimization tool applied on financial data, to appear in Pacific Journal of Optimization, 9(3), pp. 535–552, 2013.

    Google Scholar 

  44. A. Özmen, G.-W. Weber, Z. Çavuşoğlu and Ö. Defterli, The new robust conic GPLM method with an application to finance: prediction of credit default, Journal of Global Optimization, 56(2), pp. 233–249, 2013.

    Article  Google Scholar 

  45. A. Özmen and G.-W. Weber, RMARS: Robustication of Multivariate Adaptive Regression Spline, and an application in finance, Journal of Computational and Applied Mathematics, 259, pp. 914–924, 2014.

    Article  Google Scholar 

  46. M. Partner, N. Kashtan and U. Alon, Environmental variability and modularity of bacterial metabolic network, BMC Evolutionary Biology 7(169), 2007.

    Google Scholar 

  47. S. Pickl and G.-W. Weber, Optimization of a time-discrete nonlinear dynamical system from a problem of ecology - an analytical and numerical approach, Journal of Computational Technologies, 6(1), pp. 43–52, 2001.

    Google Scholar 

  48. S. Pickl, An iterative solution to the nonlinear time-discrete TEM model - the occurence of chaos and a control theoretic algorithmic approach, AIP Conference Proceedings, 627(1), pp. 196–205, 2002.

    Article  Google Scholar 

  49. I. Popescu, Robust mean-covariance solutions for stochastic optimization, Operations Research, 55 (1), 98–112, 2007.

    Article  Google Scholar 

  50. C. Roos, T. Terlaky and J. Vial, Interior point approach to linear optimization: theory and algorithms, John Wiley and Sons, New York, 1997.

    Google Scholar 

  51. C. Roos, T. Terlaky and J. Vial, Interior Point Methods for Linear Optimization, Springer Science, Heidelberg/Boston, 2006.

    Google Scholar 

  52. E. Sakamoto and H. Iba, Inferring a system of differential equations for a gene regulatory network by using genetic programming, Proceeding of Congress on Evolutionary Computing 01, pp. 720–726, 2001.

    Google Scholar 

  53. P. Taylan, G.-W. Weber and A. Beck, New approaches to regression by generalized additive models and continuous optimization for modern applications in finance, science and technology, Journal Optimization 56, 5–6, pp. 1–24, 2007.

    Google Scholar 

  54. O. Uğur, S. W. Pickl, G.-W. Weber and R. Wünschiers, An algorithmic approach to analyze genetic networks and biological energy production: an introduction and contribution where OR meets biology, Optimization, 58(1), pp. 1–22, 2009.

    Article  Google Scholar 

  55. O. Uğur and G.-W. Weber, Optimization and dynamics of gene-environment networks with intervals. Journal of Industrial Management and Optimization 3(2), pp. 357–379, 2007.

    Article  Google Scholar 

  56. G.-W. Weber, S. Z. Alparslan-Gök and B. Söyler, A new mathematical approach in environmental and life sciences: gene-environment networks and their dynamics, Environmental Modeling and Assesment, 14(2), pp. 267–288, 2007.

    Article  Google Scholar 

  57. G.-W. Weber, İ. Batmaz, G. Köksal, P. Taylan and F. Yerlikaya, CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization, IPSE 20 (3), pp. 371–400, 2012.

    Google Scholar 

  58. G.-W. Weber, S.Z. Alparslan-Gök and N. Dikmen, Environmental and life sciences: gene-environment networks - optimization, games and control - a survey on recent achievements, Journal of Organisational Transformation and Social Change, 5(3), pp. 197–233, 2008.

    Article  Google Scholar 

  59. G.-W. Weber, P. Taylan, S.-Z. Alparslan-Gök, S. Özöğür and B. Akteke-Öztürk, Optimization of gene-environment networks in the presence of errors and uncertainty with Chebychev approximation. TOP, the Operational Research journal of SEIO (Spanish Statistics and Operations Research Society) 16(2), pp. 284–318, 2008.

    Google Scholar 

  60. G.-W. Weber, S. Özögür-Akyüz and E. Kropat, A review on data mining and continuous optimization applications in computational biology and medicine. Embryo Today, Birth Defects Research (Part C) 87, pp. 165–181, 2009.

    Google Scholar 

  61. G.-W. Weber, S. Akyüz-Özöğür and E. Kropat, A review on data mining and continuous optimization applications in computational biology and medicine, Birth Defects Research (Part C)-Embryo Today, 87(2), pp. 165–181, 2009b.

    Google Scholar 

  62. G.-W. Weber, E. Kropat, A. Tezel, and S. Belen, Optimization applied on regulatory and eco-finance networks - survey and new developments, Pacific Journal of Optimization, 6(2), pp. 319–340, 2010.

    Google Scholar 

  63. R. Werner, Cascading: an adjusted exchange method for robust conic programming, CEJOR, 16, pp.179–189, 2008.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ankara, Turkey

    Ayşe Özmen

Authors
  1. Ayşe Özmen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Özmen, A. (2016). Introduction. In: Robust Optimization of Spline Models and Complex Regulatory Networks. Contributions to Management Science. Springer, Cham. https://doi.org/10.1007/978-3-319-30800-5_1

Download citation

Publish with us

Policies and ethics