14th IFAC Symposium on System Identification, SYSID 2006

SYSID-2006 Paper Abstract

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Paper FrB1.1

Steinke, Florian (Max-Planck-Inistitue for Biological Cybernetics), Schölkopf, Bernhard (Max-Planck-Inistitue for Biological Cybernetics)

Machine Learning Methods for Estimating Operator Equations

Scheduled for presentation during the Regular Session "Kernel Based Nonlinear System Identification" (FrB1), Friday, March 31, 2006, 15:30−15:50, Concert Hall

14th IFAC Symposium on System Identification, March 29 - 31, 2006, Newcastle, Australia

This information is tentative and subject to change. Compiled on September 24, 2018

Keywords Machine Learning and Data Mining, Continuous Time System Estimation, Nonparametric Methods

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.