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Machine Learning Methods For Estimating Operator Equations

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Steinke,  F
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Steinke, F., & Schölkopf, B. (2006). Machine Learning Methods For Estimating Operator Equations. In IFAC Proceedings Volumes (pp. 1192-1197). Oxford, United Kingdom: Elsevier.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D27F-B
Abstract
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.