Jörg C. Lemm
Institut für Theoretische Physik I,
D-48149 Münster, Germany
Gaussian processes have recently become
popular in the empirical learning community.
They encompass many classical methods of statistics,
e.g., radial basis functions or various splines,
and are technically convenient
due to the fact that Gaussian integrals can be performed analytically
and the corresponding saddle point equations
(to be solved for a maximum a-posteriori approximation
or empirical risk minimization)
are linear. At the same time, however, this technical advantage implies a severe
i.e., quadratic and therefore convex error surfaces,
forbid the implementation
of genuine non-convex prior knowledge.
For example, one may want to implement the belief that
individual earthquakes or electrocardiograms
tend to be similar to either a prototype
OR a prototype
(or non-zero mean Gaussian processes
in Bayesian interpretation)
are used as building blocks
for implementation of
non-convex prior knowledge
exploring possibilities to go beyond Gaussian processes.
Continuous data functions are introduced
based on the observation that
learning is, implicitly or explicitly,
based on an infinite number of data.
It is shown how empirical measurement
of an infinite amount of data
is possible by a-posteriori control.