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The International Conference on Engineering Optimization (EngOpt 2008)

Infinite kernel learning via infinite and semi-infinite programming

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Pages 937-970 | Received 11 Sep 2008, Accepted 05 Nov 2009, Published online: 03 Mar 2010

References

  • Anderson , E. J. and Nash , P. 1987 . Linear Programming in Infinite-Dimensional Spaces , New York : John Wiley and Sons Ltd .
  • Apostol , T. M. 1974 . Mathematical Analysis: A Modern Approach to Advanced Calculus , Addison Wesley .
  • Argyriou , A. , Hauser , R. , Micchelli , C. A. and Pontil , M. A DC-programming algorithm for kernel selection . 23rd International Conference on Machine Learning . Pittsburgh, PA.
  • Aster , A. , Borchers , B. and Thurber , C. 2004 . Parameter Estimation and Inverse Problems , Burlington, MA : Elsevier Academic Press .
  • Bach , F. R. and Lanckriet , G. R.G. Multiple kernel learning, conic duality, and the smo algorithm . International Conference on Machine Learning . Banff, Canada.
  • C.-C. Chang and C.-J. Lin, LIBSVM: A library for support vector machines, 2001; software available at http://www.csie.ntu.edu.tw/cjlin/libsvm
  • Chen , C.-T. 1999 . Linear System Theory and Design , New York : Oxford University Press .
  • Chen , W. , Ma , C. and Ma , L. 2009 . Mining the customer credit using hybrid support vector machine technique . Expert Syst. Appl. , : 7611 – 7616 .
  • Cristianini , N. and Shawe-Taylor , J. 2000 . An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods , Cambridge, , UK : Cambridge University Press .
  • Dudley , R. M. 1989 . Real Analysis and Probability , Cambridge, , UK : Cambridge University Press .
  • Goberna , M. A. and Lopez , M. A. 1998 . Linear Semi-Infinite Optimization , New York : John Wiley and Sons Ltd .
  • Hamilton , R. S. 1982 . The inverse function theorem of Nash and Moser . Bull. Amer. Math. Soc. (M.S.) , 7 ( 1 ) : 99 – 132 .
  • Hastie , T. , Tibshirani , R. and Friedman , J. 2001 . The Elements of Statistical Learning – Data Mining, Inference and Prediction , Springer Series in Statistics New York : Springer .
  • Hettich , R. and Jongen , H. Th. 1978 . “ Semi-infinite programming: Conditions of optimality and applications ” . In Optimization Techniques 2 , Edited by: Stoer , J. 1 – 11 . Berlin, Heidelberg, New York : Springer . Lecture notes in Control and Information Science
  • Hettich , R. and Kortanek , O. 1993 . Semi-infinite programming: Theory, methods and applications . SIAM Rev. , 35 ( 3 ) : 380 – 429 .
  • Hettich , R. and Zencke , P. 1982 . Numerische Methoden der Approximation und semi-infiniten Optimierung , Stuttgart : Teubner .
  • Kropat , E. , Weber , G. W. and Akteke-Öztürk , B. Eco-finance networks under uncertainty . EngOpt 2008 – International Conference on Engineering Optimization . June 1–5 , Rio de Janeiro, Brazil.
  • Lanckriet , G. R.G. , Cristianini , N. , Ghaoui , L. E. , Bartlett , P. and Jordan , M. I. 2004 . Learning the kernel matrix with semidefinite programming . J. Mach. Learn. Res. , 5 : 27 – 72 .
  • Linde , W. 1983 . Probability in Banach Spaces – Stable and Infinitely Divisible Distributions , Chichester, NY : John Wiley and Sons .
  • Ortega , J. M. 1977 . Numerical Analysis: A second course , New York : Academic Press, SIAM .
  • Ortega , J. M. and Reinboldt , W. C. 1970 . Iterative Solution of Nonlinear Equations with Multiple Variables , New York : Academic Press .
  • S. Özöğür-Akyüz, A mathematical contribution of statistical learning and continuous optimization using infinite and semi-infinite programming to computational statistics, Ph.D. Thesis, Middle East Technical University, Institute of Applied Mathematics, Turkey, 2009
  • Özöğür , S. , Shawe-Taylor , J. , Weber , G.-W. and Ögel , Z. B. 2009 . Pattern analysis for the prediction of eukoryatic pro-peptide cleavage sites . Discrete Appl. Math. , 157 : 2388 – 2394 .
  • Özöğür-Akyüz , S. , Hussain , Z. and Shawe-Taylor , J. 2010 . “ Prediction with the SVM using test point margins ” . In Annals of Information Systems 8: Data Mining , Edited by: Stahlbock , R. , Crone , S. V. and Lessmann , S. 147 – 158 . Hamburg : Springer .
  • Parthasarathy , K. R. 2005 . Probability Measures on Metric Spaces , Providence, RI : AMS Chelsea Publishing .
  • Rakotomamonjy , A. , Bach , F. , Canu , S. and Grandvalet , Y. More efficiency in multiple kernel learning . 24th International Conference on Machine Learning . Corvallis.
  • Schölkopf , B. and Smola , A. J. 2002 . Learning with Kernels , MA, USA : MIT Press .
  • J. Shawe-Taylor, Review of Anthony Martin; Bartlett Peter L. 2001 . Neural Network Learning: Theoretical Foundations , Cambridge, , UK : Cambridge University Press .
  • Shawe-Taylor , J. and Cristianini , N. 2004 . Kernel Methods for Pattern Analysis , Cambridge, , UK : Cambridge University Press .
  • Shiryaev , A. N. 1995 . Probability , New York : Springer Verlag .
  • E.M. Silvia., Riemann-stieltjes integration, Technical report, UC Davis, One Shields Avenue, Davis, 1999
  • Sonnenburg , S. , Raetsch , G. , Schafer , C. and Schöelkopf , B. 2006 . Large scale multiple kernel learning . J. Mach. Learn. Res. , 7 : 1531 – 1565 .
  • Still , G. 2004 . Semi-infinite programming: An introduction, preliminary version . Technical Report ,
  • Takeda , A. and Kanamori , T. 2009 . A robust approach based on conditional value-at-risk measure to statistical learning problems . Eur. J. Oper. Res. , 198 : 287 – 296 .
  • Taylan , P. and Weber , G.-W. 2007 . New approaches to regression in financial mathematics by additive models . J. Comput. Technol. , 12 ( 2 ) : 3 – 22 .
  • Taylan , P. , Weber , G.-W. and Beck , A. 2007 . New approaches to regression by generalized additive models and continuous optimization for modern applications in finance, science and techology . Optimization , 56 ( 5&6 ) : 675 – 698 .
  • Taylan , P. , Weber , G.-W. and Yerlikaya , F. Continuous optimization applied in MARS for modern application in finance, science and technology . Continuous Optimization and Knowledge Based Technologies, 20th EURO Mini conference . Lithuania. pp. 317 – 322 .
  • Vapnik , V. N. 1998 . Statistical Learning Theory , John Wiley and Sons .
  • Varga , R. S. 2000 . Matrix Iterative Analysis , Springer .
  • Wan , Z. , Wu , S. Y. and Teo , K. L. 2007 . Some properties on quadratic infinite programs of integral type . Appl. Math. Lett. , 20 : 676 – 680 .
  • Weber , G.-W. 1992 . “ Charakterisierung struktureller Stabilität in der nichtlinearen Optimierung ” . In Aachener Beitraege zur Mathematik 5 , Edited by: Bock , H. H. , Jongen , H. Th. and Plesken , W. Aachen : Augustinus publishing house (now: Mainz Publishing House) .
  • Weber , G.-W. 1993 . “ Minimization of a max-type function: Characterization of structural stability ” . In Parametric Optimization and Related Topics III , Edited by: Guddat , J. , Jongen , H. Th. , Kummer , B. and Nozicka , F. 519 – 538 . Frankfurt a.m., Bern : Peter Lang publishing house .
  • Weber , G. W. 2003 . Generalized Semi-Infinite Optimization and Related Topics , Vol. 29 , Germany : Heldermann Verlag . Research and Exposition in Mathematics
  • Weber , G.-W. , Taylan , P. , Özöğür , S. and Akteke-Öztürk , B. 2007 . “ Statistical learning and optimization methods in data mining ” . In Recent Advances in Statistics , Edited by: Ayhan , H. O. and Batmaz , I. 181 – 195 . Ankara : Turkish Statistical Institute Press .
  • Wetterling , W. W.E. 1970 . Definitheitsbedingungen für relative Extrema bei Optimierungs und Approximationsaufgaben . Numer. Math. , 12 : 122 – 136 .
  • Yerlikaya , F. , Weber , G.-W. , Taylan , P. , Batmaz , İ. and Köksal , G. MARS Algoritmasında Tikhonov Düzenlemesi ve çok Amaçlı Optimizasyon Kullanımı . Proceedings of Operational Research and Industrial Engineering Annual Conference (YA/EM’08) Galatasaray University . 30 June–2 July , Istanbul, Turkey. (on a CD)

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