Abstract
Logistic regression is presumably the most popular representative of probabilistic discriminative classifiers. In this paper, a kernel variant of logistic regression is introduced as an iteratively re-weighted least-squares algorithm in kernel-induced feature spaces. This formulation allows us to apply highly efficient approximation methods that are capable of dealing with large-scale problems. For multi-class problems, a pairwise coupling procedure is proposed. Pairwise coupling for “kernelized” logistic regression effectively overcomes conceptual and numerical problems of standard multi-class kernel classifiers.
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References
D.R. Cox and E. J. Snell. Analysis of Binary Data. Chapman & Hall, London, 1989.
T. Jaakkola, M. Meila, and T. Jebara. Maximum entropy discrimination. In S.A. Solla, T.K. Leen, and K.-R. Müller, editors, Advances in Neural Information Processing Systems, volume 12, pages 470–476. MIT Press, 1999.
P. Sollich. Probabilistic methods for support vector machines. In S.A. Solla, T.K. Leen, and K.-R. Müller, editors, Advances in Neural Information Processing Systems, volume 12, pages 349–355. MIT Press, 1999.
L. Hermes, D. Frieauff, J. Puzicha, and J. Buhmann. Support vector machines for land usage classification in Landsat TM imagery. In Proc. of the IEEE 1999 International Geoscience and Remote Sensing Symposium, volume 1, pages 348–350, 1999.
V. Roth and V. Steinhage. Nonlinear discriminant analysis using kernel functions. In S.A. Solla, T.K. Leen, and K.-R. Müller, editors, Advances in Neural Information Processing Systems, volume 12, pages 568–574. MIT Press, 1999.
S. Mika, G. Rätsch, J. Weston, B. Schölkopf, and K.-R. Müller. Fisher discriminant analysis with kernels. InY.-H. Hu, J. Larsen, E. Wilson, and S. Douglas, editors, Neural Networks for Signal Processing IX, pages 41–48. IEEE, 1999.
Trevor Hastie and Robert Tibshirani. Classification by pairwise coupling. In Michael I. Jordan, Michael J. Kearns, and Sara A. Solla, editors, Advances in Neural Information Processing Systems, volume 10. The MIT Press, 1998.
K.-R. Müller, S. Mika, G. Rätsch, K. Tsuda, and B. Schölkopf. An introduction to kernelbased learning algorithms. IEEE Transactions on Neural Networks, 12(2): 181–201, March 2001.
M.R. Osborne. Fisher's method of scoring. Internat. Statistical Review, 60: 99–117, 1992.
I. Nabney. Efficient training of RBF networks for classification. Technical Report NCRG/99/002, Aston University, Birmingham, UK., 1999.
A.E. Hoerl and R.W. Kennard. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12: 55–67, 1970.
W.H. Press, S.A. Teukolsky, W.T Vetterling, and B.P. Flannery. Numerical Recipes in C. Cambridge University Press, 1992.
T. Jaakkola and D. Haussler. Probabilistic kernel regression models. In David Heckerman and Joe Whittaker, editors, Procs. 7th International Workshop on AI and Statistics. Morgan Kaufmann, 1999.
R. J. Vanderbei. LOQO: An interior point code for quadratic programming. Optimization Methods and Software, 11: 451–484, 1999.
Ronan Collobert and Samy Bengio. Support vector machines for large-scale regression problems. Technical Report IDIAP-RR-00-17, IDIAP, Martigny, Switzerland, 2000.
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Roth, V. (2001). Probabilistic Discriminative Kernel Classifiers for Multi-Class Problems. In: Radig, B., Florczyk, S. (eds) Pattern Recognition. DAGM 2001. Lecture Notes in Computer Science, vol 2191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45404-7_33
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DOI: https://doi.org/10.1007/3-540-45404-7_33
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