  A new general framework is presented for implementing complex a priori
knowledge, having in mind especially situations where the number of available
training data is small compared to the complexity of the learning task. A
priori information is hereby decomposed into simple components represented by
quadratic building blocks (quadratic concepts) which are then combined by
conjunctions and disjunctions to built more complex, problem specific error
functionals. While conjunction of quadratic concepts leads to classical
quadratic regularization functionals, disjunctions, representing ambiguous
priors, result in non--convex error functionals. These go beyond classical
quadratic regularization approaches and correspond, in Bayesian interpretation,
to non--gaussian processes. Numerical examples show that the resulting
stationarity equations, despite being in general nonlinear, inhomogeneous
(integro--)differential equations, are not necessarily difficult to solve.
Appendix A relates the formalism of statistical mechanics to statistics and
Appendix B describes the framework of Bayesian decision theory.
