Machine Learning Methods for Estimating Operator Equations
Florian Steinke and Bernhard Schölkopf
In: 14th IFAC (International Federation of Automatic Control) Symposium on System Identification, SYSID 2006, 29-31 March 2006, Newcastle, Australia.
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.