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Original Articles

Spline regression models for complex multi-modal regulatory networks

, &
Pages 515-534 | Received 04 Jun 2012, Accepted 17 Jun 2013, Published online: 20 Aug 2013

REFERENCES

  • R.C. Aster, B. Borchers, and C. Thurber, Parameter Estimation and Inverse Problems, Academic Press, Boston, MA, 2004.
  • L. Breiman, J.H. Friedman, R. Olshen, and C. Stone, Classification and Regression Trees, Wadsworth Int. Group, Belmont, CA, 1984.
  • T. Chen, H.L. He, and G.M. Church, Modeling gene expression with differential equations, Proc. Pacific Symp. Biocomput. 4 (1999), pp. 29–40.
  • R.D. De Veaux, D.C. Psichogios, and L.H. Ungar, A comparison of two non- parametric schemes: MARS and neural networks, Comput. Chem. Eng. 17 (1993), pp. 819–837. doi: 10.1016/0098-1354(93)80066-V
  • J.H. Friedman, Multivariate adaptive regression splines, The Ann. Stat. 19 (1) (1991), pp. 1–141. doi: 10.1214/aos/1176347963
  • J. Gebert, M. Latsch, S.W. Pickl, G.-W. Weber, and R. Wünschiers, Genetic networks and anticipation of gene expression patterns, AIP Conf. Proc. 718 (2004), pp. 474–485. doi: 10.1063/1.1787351
  • T. Hastie and R.J. Tibshirani, Discriminant analysis by Gaussian mixtures, J. R. Stat. Soc. (Ser. B) 58 (1996), pp. 155–176.
  • T. Hastie, R. Tibshirani, and J.H. Friedman, The Element of Statistical Learning, Springer-Verlag, New York, 2001.
  • 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, Proc. Pacific Symp. Biocomput. 8 (2003), pp. 17–28.
  • M. Kriner, Survival analysis with multivariate adaptive regression splines, Dissertation, LMU Mnchen: Faculty of Mathematics, Comput. Sci. Stat., 2007.
  • E. Kropat, G.-W. Weber, and S. Belen, Dynamical gene-environment networks under ellipsoidal uncertainty—set-theoretic regression analysis based on ellipsoidal OR, in Dynamics, Games and Science I, M. Peixoto, D. Rand and A. Pinto, eds., Springer-Verlag, Berlin, 2011, pp. 545–571.
  • E. Kropat, G.-W. Weber, and C.S. Pedamallu, Regulatory networks under ellıpsoidal uncertainty—data analysis and prediction by optimization theory and dynamical systems, in Data Mining: Foundations and Intelligent Paradigms, D.E. Holmes and L.C. Jain, eds., Springer-Verlag, Berlin 2012, pp. 27–56.
  • J.R. Leathwicka, J. Elith, and T. Hastie, Comparative performance of generalized additive models and multivariate adaptive regression splines for statistical modelling of species distributions, Ecol. Model. 199 (2) (1993), pp. 188–196. doi: 10.1016/j.ecolmodel.2006.05.022
  • MARS® Salford Systems; software. Available at http://www.salfordsystems.com
  • MOSEK™; software. Available at http://www.mosek.com
  • A. Özmen, Robust conic quadratic programming applied to quality improvement—a robustification of CMARS, MSc thesis, Middle East Technical University, 2010.
  • A. Özmen, G.-W. Weber, I. Batmaz, and E. Kropat, RCMARS: Robustification of CMARS with different scenarios under polyhedral uncertainty set, Commun. Nonlinear Sci. Num. Simul. 16 (12) (2011), pp. 4780–4787. doi: 10.1016/j.cnsns.2011.04.001
  • A. Özmen, I. Batmaz, and G.-W. Weber, Robust conic multivariate adaptive regression splines (RCMARS) and an application to precipitation modeling, Technical Report, IAM, METU, 2012, submitted to Environ. Model. Assess.
  • A. Özmen, G.-W. Weber, and A. Karimov, A new robust optimization tool applied on financial data, Technical Report, IAM, METU, 2011, to appear in Pac. J. Optim.
  • C. Roos, T. Terlaky, and J. Vial, Interior Point Approach to Linear Optimization: Theory and Algorithms, John Wiley & Sons, New York, 1997.
  • C. Roos, T. Terlaky, and J. Vial, Interior Point Methods for Linear Optimization, Springer Science, Heidelberg, 2006.
  • E. Sakamoto and H. Iba, Inferring a system of differential equations for a gene regulatory network by using genetic programming, Proc. Congress Evol. Comput.’ 01 (2001), pp. 720–726.
  • 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, Optimization. 56(5–6) (2007), pp. 675–698. doi: 10.1080/02331930701618740
  • P. Taylan, G.-W. Weber, and F. Yerlikaya-Özkurt, A new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimization, Top 18 (2010), pp. 377–395. doi: 10.1007/s11750-010-0155-7
  • O. Uğur and G.-W. Weber, Optimization and dynamics of gene-environment networks with intervals, J. Ind. Manag. Optim. 3(2) (2007), pp. 357–379. doi: 10.3934/jimo.2007.3.357
  • O. Uğur, S.W. Pickl, G.-W. Weber, and R. Wünschiers, An algorithmic approach to analyse genetic networks and biological energy production: An introduction and contribution where OR meets biology, Optimziation 58(1) (2009), pp. 1–22. doi: 10.1080/02331930701761169
  • G.-W. Weber, A. Tezel, P. Taylan, A. Söyler, and M. Çetin, Mathematical contributions to dynamics and optimization of gene-environment networks, Optimization 57(2) (2008), pp. 353–377. doi: 10.1080/02331930701780037
  • G.-W. Weber, O. Uğur, P. Taylan, and A. Tezel, On optimization, dynamics and uncertainty: A tutorial for gene-environment networks, Discret. Appl. Math. 157(10) (2009), pp. 2494–2513. doi: 10.1016/j.dam.2008.06.030
  • G.-W. Weber, E. Kropat, A. Tezel, and S. Belen, Optimization applied on regulatory and eco-finance networks—survey and new developments, Pacific J. Optim. 6(2) (2010), pp. 319–340.
  • G.-W. Weber, I. Batmaz, G. Köksal, P. Taylan, and F. Yerlikaya, CMARS: A new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization, Inverse Probl. Sci. Eng. 20(3) (2012), pp. 371–400. doi: 10.1080/17415977.2011.624770

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