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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.
