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Learning with Non-Positive Kernels


Conference Paper


n this paper we show that many kernel methods can be adapted to deal with indefinite kernels, that is, kernels which are not positive semidefinite. They do not satisfy Mercer‘s condition and they induce associated functional spaces called Reproducing Kernel Kre&icaron;n Spaces (RKKS), a generalization of Reproducing Kernel Hilbert Spaces (RKHS).Machine learning in RKKS shares many "nice" properties of learning in RKHS, such as orthogonality and projection. However, since the kernels are indefinite, we can no longer minimize the loss, instead we stabilize it. We show a general representer theorem for constrained stabilization and prove generalization bounds by computing the Rademacher averages of the kernel class. We list several examples of indefinite kernels and investigate regularization methods to solve spline interpolation. Some preliminary experiments with indefinite kernels for spline smoothing are reported for truncated spectral factorization, Landweber-Fridman iterations, and MR-II.

Author(s): Ong, CS. and Mary, X. and Canu, S. and Smola, AJ.
Book Title: ICML 2004
Journal: Proceedings of the Twenty-First International Conference on Machine Learning (ICML 2004)
Pages: 81-81
Year: 2004
Month: July
Day: 0
Publisher: ACM Press

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

DOI: 10.1145/1015330.1015443
Event Name: Twenty-First International Conference on Machine Learning
Event Place: Banff, Alberta, Canada

Address: New York, NY, USA
Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Learning with Non-Positive Kernels},
  author = {Ong, CS. and Mary, X. and Canu, S. and Smola, AJ.},
  journal = {Proceedings of the Twenty-First International Conference on Machine Learning (ICML 2004)},
  booktitle = {ICML 2004},
  pages = {81-81},
  publisher = {ACM Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {New York, NY, USA},
  month = jul,
  year = {2004},
  month_numeric = {7}