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Machine Learning Methods For Estimating Operator Equations

2006

Conference Paper

ei


We consider the problem of fitting a linear operator induced equation to point sampled data. In order to do so we systematically exploit the duality between minimizing a regularization functional derived from an operator and kernel regression methods. Standard machine learning model selection algorithms can then be interpreted as a search of the equation best fitting given data points. For many kernels this operator induced equation is a linear differential equation. Thus, we link a continuous-time system identification task with common machine learning methods. The presented link opens up a wide variety of methods to be applied to this system identification problem. In a series of experiments we demonstrate an example algorithm working on non-uniformly spaced data, giving special focus to the problem of identifying one system from multiple data recordings.

Author(s): Steinke, F. and Schölkopf, B.
Book Title: Proceedings of the 14th IFAC Symposium on System Identification (SYSID 2006)
Journal: Proceedings of the 14th IFAC Symposium on System Identification (SYSID 2006)
Pages: 6
Year: 2006
Month: March
Day: 0
Editors: B Ninness and H Hjalmarsson
Publisher: Elsevier

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

Event Name: 14th IFAC Symposium on System Identification (SYSID 2006)
Event Place: Newcastle, Australia

Address: Oxford, United Kingdom
Digital: 0
Institution: International Federation of Automatic Control (IFAC)
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{3640,
  title = {Machine Learning Methods For Estimating Operator Equations},
  author = {Steinke, F. and Sch{\"o}lkopf, B.},
  journal = {Proceedings of the 14th IFAC Symposium on System Identification (SYSID 2006)},
  booktitle = {Proceedings of the 14th IFAC Symposium on System Identification (SYSID 2006)},
  pages = {6},
  editors = {B Ninness and H Hjalmarsson},
  publisher = {Elsevier},
  organization = {Max-Planck-Gesellschaft},
  institution = {International Federation of Automatic Control (IFAC)},
  school = {Biologische Kybernetik},
  address = {Oxford, United Kingdom},
  month = mar,
  year = {2006},
  month_numeric = {3}
}