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Support Vector Regression

Support Vector Regression. SVR. Drawings and illustrations from Bernhard Schölkopf, and Alex Smola: Learning with Kernels (MIT Press, Cambridge, MA, 2002). SVR - History. Based on Learning Theory, consisting of few axioms on learning errors Started in 1960’s, still actively developed

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Support Vector Regression

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  1. Support Vector Regression ACAT02, Moscow

  2. SVR Drawings and illustrations from Bernhard Schölkopf, and Alex Smola: Learning with Kernels (MIT Press, Cambridge, MA, 2002) ACAT02, Moscow

  3. SVR - History • Based on Learning Theory, • consisting of few axioms on learning errors • Started in 1960’s, still actively developed • SVRs recently outperformed NNs in recognition tests on US Postal Service’s standard set of handwritten characters • libSVM by Chih-Chung Chang and Chih-Jen Lin provides fast and simple to use implementation, extended as requests (e.g. from HEP) come in ACAT02, Moscow

  4. Formulation of Problem • Training sample X, observed results Y • Goal: f with y=f(x) • Simplicity: • Linear case, ACAT02, Moscow

  5. Optimizing the Confidence Optimal confidence = maximal margin Minimize quadratic problem with Quadratic problem: Unique solution! ACAT02, Moscow

  6. Non-Linearity Introduce mapping to higher dimensional space e.g. Gaussian kernel: ACAT02, Moscow

  7. Calculation ACAT02, Moscow

  8. L2 b Tagger Parameters ACAT02, Moscow

  9. L2 b Tagger Parameters ACAT02, Moscow

  10. L2 b Tagger Output SVR NN ACAT02, Moscow

  11. L2 b Tagger Discussion • Complex problem increases number of SVs • Almost non-separable classes still almost non-separable in high dimensional space • High processing time due to large number of SVs • NNs show better performance for low-information, low-separability problems ACAT02, Moscow

  12. Higgs Parameters Higgs SVR analysis by Daniel Whiteson, UC Berkley ACAT02, Moscow

  13. Higgs Parameters ACAT02, Moscow

  14. Higgs Output  Background Signal   Background Signal  ACAT02, Moscow

  15. Higgs Purity / Efficiency Purity ACAT02, Moscow

  16. Kernel Width Integrated Significance Kernel Width ACAT02, Moscow

  17. Summary • SVR often superior to NN • Not stuck in local minima: unique solution • Better performance for many problems • Implementation exists, actively supported by the development community • Further information: www.kernel-machines.org Time for SVR @ HEP! ACAT02, Moscow

  18. L2 b Tagger Correlation NN NN SVR SVR b udcs ACAT02, Moscow

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